AGREEMENT

Exhibit 10.1

EXECUTION VERSION

AGREEMENT

This Agreement (this “Agreement”) is made and entered into as of June 19, 2012, by and among Integrated Device Technology, Inc. (the “Company”) and the entities and natural persons listed on Exhibit A hereto and their Affiliates (as defined herein) (collectively, “Starboard”) (each of the Company and Starboard, a “Party” to this Agreement, and collectively, the “Parties”).

RECITALS:

WHEREAS, the Company and Starboard have engaged in various discussions and communications concerning the Company’s business, financial performance and strategic plans;

WHEREAS, Starboard is deemed to beneficially own shares of common stock of the Company (the “Common Stock”) totaling, in the aggregate, 12,150,000 shares, or approximately 8.5% of the Common Stock issued and outstanding on the date hereof;

WHEREAS, Starboard submitted a nomination letter to the Company on June 15, 2012 (the “Nomination Letter”) nominating director candidates to be elected to the Company’s board of directors (the “Board”) at the 2012 annual meeting of stockholders of the Company (the “2012 Annual Meeting”); and

WHEREAS the Company and the members of Starboard have determined to come to an agreement with respect to the composition of the Board, certain matters related to the 2012 Annual Meeting and certain other matters, as provided in this Agreement.

NOW, THEREFORE, in consideration of the foregoing premises and the mutual covenants and agreements contained herein, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Parties hereto, intending to be legally bound hereby, agree as follows:

(a) The Company agrees that the Board and all applicable committees of the Board shall take all necessary action, (i) effective immediately following execution of this Agreement, to increase the size of the Board from seven (7) to nine (9) members and appoint Peter A. Feld (“Appointee One”) and Jeffrey S. McCreary as members of the Board (collectively, the “New Appointees”). The Company further agrees that prior to the time that it mails its definitive proxy statement for the 2012 Annual Meeting, the Board shall take all necessary action, subject to Section 1(b), (g) and (i) below, to nominate the New Appointees for election to the Board at the 2012 Annual Meeting. The Company further agrees that the Board and all applicable committees of the Board will nominate no more than nine (9) members for election to the Board at the 2012 Annual Meeting, inclusive of the New Appointees.

(b) Prior to the appointment and nomination of the New Appointees by the Board in accordance with Section 1(a), the Nominating & Governance Committee of the Board (the

“Nominating & Governance Committee”) shall have reviewed and reasonably approved, in accordance with the Company’s corporate governance guidelines and the charter of the Nominating & Governance Committee, the qualifications of the New Appointees to serve as members of the Board and recommended to the Board that the Board (i) appoint the New Appointees and (ii) nominate the New Appointees for election at the 2012 Annual Meeting, in each case in accordance with Section 1(a).

(c) The Company agrees that the New Appointees shall be considered by the Board for Board committee appointment in connection with the Board’s annual review of committee composition. Specific committee assignments would be determined by the Board in accordance with the Company’s corporate governance guidelines and applicable committee charters and in compliance with applicable securities laws. Notwithstanding the foregoing, Appointee One shall be appointed to the Nominating & Governance Committee concurrent with his appointment to the Board pursuant to Section 1(a).

(d) The Company shall work to identify an additional director candidate who will (i) qualify as “independent” pursuant to NASDAQ listing standards and (ii) have relevant financial and business experience (the “Additional Appointee”); such candidate shall be reviewed in accordance with the Company’s corporate guidelines and the charter of the Nominating & Governance Committee and unanimously approved by the Nominating & Governance Committee for recommendation to the full Board for appointment or nomination, as applicable. In the event that the Company has identified the Additional Appointee prior to the time that the Company mails its definitive proxy statement for the 2012 Annual Meeting, then the Additional Appointee will be nominated for election to the Board at the 2012 Annual Meeting. In the event that the Company has not identified the Additional Appointee prior to the time that the Company mails its definitive proxy statement for the 2012 Annual Meeting, then the Board and all applicable committees of the Board will nominate no more than eight (8) members for election to the Board at the 2012 Annual Meeting, inclusive of the New Appointees, and the Company will continue to work towards identifying and approving an Additional Appointee to be appointed to the Board after the 2012 Annual Meeting pursuant to this Section 1(d).

(e) Upon execution of this Agreement, Starboard hereby withdraws its Nomination Letter and Starboard agrees not to (i) nominate any person for election at the 2012 Annual Meeting or (ii) submit any proposal for consideration at, or bring any other business before, the 2012 Annual Meeting, directly or indirectly. Starboard shall not publicly or privately encourage or support any other stockholder to nominate any person for election at the 2012 Annual Meeting.

(f) The Company agrees that it will recommend, support and solicit proxies for the election of the New Appointees at the 2012 Annual Meeting in the same manner as for the Company’s other nominees who are up for election.

(g) The Company agrees that if either of the New Appointees is unable to serve as a director, resigns as a director or is removed as a director prior to the 2013 annual meeting of stockholders of the Company (the “2013 Annual Meeting”) and at such time Starboard beneficially owns in the aggregate at least the lesser of 3.0% of the Company’s then outstanding Common Stock and 4,268,157 shares of Common Stock (subject to adjustment for stock splits,

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reclassifications and similar adjustments), Starboard shall have the ability to recommend a substitute person(s); provided that, (i) any substitute for Appointee Two will qualify as “independent” pursuant to NASDAQ listing standards, (ii) any substitute has relevant financial and business experience to fill the resulting vacancy and (iii) in each case subject to the approval of the Nominating & Governance Committee in good faith after exercising its fiduciary duties, which approval shall not be unreasonably withheld (any such replacement nominee appointed in accordance with the provisions of this clause (e) shall be referred to as the “Replacement Director”). In the event the Nominating & Governance Committee does not accept a substitute person recommended by Starboard, Starboard will have the right to recommend additional substitute person(s) for consideration by the Nominating & Governance Committee. Upon the acceptance of a replacement director nominee by the Nominating & Governance Committee, the Board will appoint such replacement director to the Board no later than five business days after the Nominating & Governance Committee recommendation of such replacement director.

(h) At the 2012 Annual Meeting, Starboard agrees to appear in person or by proxy and vote all shares of Common Stock of the Company beneficially owned by it and its Affiliates (i) in favor of the election of each of the Company’s nominees for election to the Board (ratably with respect to all nominees) and (ii) for each other proposal to come before the respective annual meeting in accordance with the Board’s recommendation, unless, as relates solely to the proposals other than the election of directors, Institutional Shareholder Services Inc. (“ISS”) recommends otherwise, in which case Starboard shall be permitted to vote all shares of Common Stock of the Company beneficially owned by it and its Affiliates in accordance with the ISS recommendation if, after discussing the proposals with the Company in good faith, Starboard subsequently decides to follow the ISS recommendation rather than the Board’s recommendation.

(i) Starboard agrees to obtain from Appointee One an irrevocable resignation letter pursuant to which Appointee One shall resign from the Board and all applicable committees thereof if at any time prior to the conclusion of the 2013 Annual Meeting Starboard’s aggregate beneficial ownership of Common Stock decreases to less than the lesser of 3.0% of the Company’s then outstanding Common Stock and 4,268,157 shares of Common Stock (subject to adjustment for stock splits, reclassifications and similar adjustments). Also at such time, the right of Starboard to recommend a Replacement Director to fill the vacancy caused by any such resignation of Appointee One pursuant to Section 1(g) shall automatically terminate.

(a) Each member of Starboard agrees that, from the date of this Agreement until the earlier of (i) the date that is fifteen (15) business days prior to the deadline for the submission of stockholder nominations for the 2013 Annual Meeting pursuant to the Company’s bylaws or (ii) the date that is one-hundred (100) days prior to the first anniversary of the 2012 Annual Meeting (the “Standstill Period”) neither it nor any of its Affiliates or Associates (as such terms are defined in Regulation 14A under the Securities Exchange Act of 1934, as amended or the rules or regulations thereunder (the “Exchange Act”)) under its control or direction will, and it will cause each of its Affiliates and Associates under its control not to, directly or indirectly, in any manner:

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(i) alone or with others, control, seek to control or seek representation on the Board (except as specifically contemplated in Section 1);

(ii) engage in any solicitation of proxies or consents or become a “participant” in a “solicitation” as such terms are defined in Regulation 14A under the Exchange Act of proxies or consents (including, without limitation, any solicitation of consents to call a special meeting of stockholders), in each case, with respect to securities of the Company;

(iii) seek to advise, encourage, support or influence any person with respect to the voting or disposition of any securities of the Company at any annual or special meeting of stockholders, except in accordance with Section 1;

(iv) seek or encourage any person to submit nominations in furtherance of a “contested solicitation,” or take other applicable action, for the election or removal of directors with respect to the Company;

(v) (A) make any proposal for consideration by stockholders at any annual or special meeting of stockholders of the Company, (B) make any offer or proposal (with or without conditions) with respect to a merger, acquisition, disposition or other business combination involving Starboard and the Company, or encourage, initiate or support any other third party in any such related activity or (C) make any public communication in opposition to any Company acquisition or disposition activity approved by the Board;

(vi) form, join or in any way participate in any “group” (within the meaning of Section 13(d)(3) of the Exchange Act) with respect to the Common Stock (other than a “group” that includes all or some lesser number of the persons identified as part of Starboard on Exhibit A attached hereto, but does not include any other members who are not currently identified as part of Starboard as of the date hereof); provided, however, that nothing herein shall limit the ability of an Affiliate of Starboard to join the “group” following the execution of this Agreement, so long as any such Affiliate agrees to be bound by the terms and conditions of this Agreement;

(vii) deposit any Common Stock in any voting trust or subject any Common Stock to any arrangement or agreement with respect to the voting of any Common Stock, other than any such voting trust, arrangement or agreement solely among the members of Starboard; or

(viii) make any request or submit any proposal to amend the terms of this Agreement other than through non-public communications with the Company that would not be reasonably determined to trigger public disclosure obligations for any Party.

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(b) Except as expressly provided in Section 1 or Section 2(a), each member of Starboard shall be entitled to:

(i) vote their shares on any other proposal duly brought before the 2012 Annual Meeting, or otherwise vote as each member of Starboard determines in its sole discretion; or

(ii) disclose, publicly or otherwise, how it intends to vote or act with respect to any securities of the Company, any stockholder proposal or other matter to be voted on by the stockholders of the Company and the reasons therefore; provided that, as applicable, all such activity is in compliance with the requirements of Section 1 and Section 2(a).

The Company represents and warrants to Starboard that (a) the Company has the corporate power and authority to execute this Agreement and to bind it thereto, (b) this Agreement has been duly and validly authorized, executed and delivered by the Company, constitutes a valid and binding obligation and agreement of the Company, and is enforceable against the Company in accordance with its terms, except as enforcement thereof may be limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance or similar laws generally affecting the rights of creditors and subject to general equity principles and (c) the execution, delivery and performance of this Agreement by the Company does not and will not violate or conflict with (i) any law, rule, regulation, order, judgment or decree applicable to it or (ii) result in any breach or violation of or constitute a default (or an event which with notice or lapse of time or both could become a default) under or pursuant to, or result in the loss of a material benefit under, or give any right of termination, amendment, acceleration or cancellation of, any organizational document, agreement, contract, commitment, understanding or arrangement to which the Company is a party or by which it is bound.

(a) Each Starboard member represents and warrants to the Company that (i) the authorized signatories of Starboard set forth on the signature page hereto have the power and authority to execute this Agreement and to bind applicable Starboard member to this Agreement, (ii) this Agreement has been duly authorized, executed and delivered by Starboard, and is a valid and binding obligation of Starboard, enforceable against Starboard in accordance with its terms, except as enforcement thereof may be limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance or similar laws generally affecting the rights of creditors and subject to general equity principles and (iii) the execution, delivery and performance of this Agreement by Starboard does not and will not violate or conflict with (A) any law, rule, regulation, order, judgment or decree applicable to it or (ii) result in any breach or violation of or constitute a default (or an event which with notice or lapse of time or both could become a default) under or pursuant to, or result in the loss of a material benefit under, or give any right of termination, amendment, acceleration or cancellation of, any organizational document, agreement, contract, commitment, understanding or arrangement to which Starboard is a party or by which it is bound.

(b) Each Starboard member shall cause its Affiliates and Associates to comply with the terms of this Agreement.

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Promptly following the execution of this Agreement, the Company and Starboard shall jointly issue a mutually agreeable press release (the “Mutual Press Release”) announcing certain terms of this Agreement, in the form attached hereto as Exhibit B. Prior to the issuance of the Mutual Press Release, neither the Company nor Starboard shall issue any press release or public announcement regarding this Agreement without the prior written consent of the other Party. During the Standstill Period, neither the Company nor Starboard or the New Appointees shall make any public announcement or statement that is inconsistent with or contrary to the statements made in the Mutual Press Release, except as required by law or the rules of any stock exchange or with the prior written consent of the other Party; provided, however, that nothing herein will limit Starboard’s limited ability to make public announcements of the type described in Section 2(b)(ii) above.

This Agreement shall terminate and the obligations of the Parties pursuant to this Agreement shall cease on the earliest to occur of the following:

(a) at the option of the Company, provided that it is not in material breach of this Agreement at such time, upon a material breach by Starboard of any obligation pursuant to this Agreement which has not been cured within ten (10) days after Starboard receives notice of such breach from the Company;

(b) at the option of Starboard, provided that it is not in material breach of this Agreement at such time, upon a material breach by the Company of any obligation pursuant to this Agreement which has not been cured within ten (10) days after the Company receives notice of such breach from Starboard; or

(c) at any time, upon the written consent of all of the Parties.

Each of the members of Starboard, on the one hand, and the Company, on the other hand, acknowledges and agrees that irreparable injury to the other party hereto would occur in the event any of the provisions of this Agreement were not performed in accordance with their specific terms or were otherwise breached and that such injury would not be adequately compensable in damages. It is accordingly agreed that the members of Starboard or any of them, on the one hand, and the Company, on the other hand (the “Moving Party”), shall each be entitled to specific enforcement of, and injunctive relief to prevent any violation of, the terms hereof, and the other Party hereto will not take action, directly or indirectly, in opposition to the Moving Party seeking such relief on the grounds that any other remedy or relief is available at law or in equity. In the event a Party institutes any legal action to enforce such Party’s rights, or recover damage for breach of this Agreement, the prevailing Party or Parties in such action shall be entitled to recover from the other Party or Parties all out-of-pocket costs and expenses, including but not limited to reasonable attorney’s fees, court costs, witness fees, disbursements and any other expenses of litigation or negotiations incurred by such prevailing Party or Parties.

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The Company shall reimburse Starboard for its reasonable, documented out of pocket fees and expenses (including legal expenses) incurred in connection with the matters related to the 2012 Annual Meeting, the filing of a Schedule 13D in connection with this Agreement and the negotiation and execution of this Agreement; provided that, such reimbursement shall not exceed $25,000 in the aggregate. The Parties shall otherwise bear their own costs and expenses incurred in connection with matters related to the 2012 Annual Meeting and the negotiation and execution of this Agreement.

If any term, provision, covenant or restriction of this Agreement is held by a court of competent jurisdiction to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Agreement shall remain in full force and effect and shall in no way be affected, impaired or invalidated. It is hereby stipulated and declared to be the intention of the Parties that the Parties would have executed the remaining terms, provisions, covenants and restrictions without including any of such which may be hereafter declared invalid, void or unenforceable. In addition, the Parties agree to use their best efforts to agree upon and substitute a valid and enforceable term, provision, covenant or restriction for any of such that is held invalid, void or enforceable by a court of competent jurisdiction.

Any notices, consents, determinations, waivers or other communications required or permitted to be given under the terms of this Agreement must be in writing and will be deemed to have been delivered: (a) upon receipt, when delivered personally; (b) upon receipt, when sent by facsimile (provided confirmation of transmission is mechanically or electronically generated and kept on file by the sending Party); or (c) one business day after deposit with a nationally recognized overnight delivery service, in each case properly addressed to the Party to receive the same. The addresses and facsimile numbers for such communications shall be:

If to the Company:

Integrated Device Technology, Inc.

6024 Silver Creek Valley Road

San Jose, California 95138

Fax: (408)  ###-###-####

Attention: General Counsel

with a copy to (which shall not constitute notice):

Latham & Watkins LLP

140 Scott Drive

Menlo Park, California 94025

Fax: (650)  ###-###-####

Attention: Mark Roeder

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If to Starboard or any member thereof:

Starboard Value LP

830 Third Avenue, 3rd Floor

New York, New York 10022

Attention: Jeffrey C. Smith

Telephone: (212)  ###-###-####

Facsimile: (212)  ###-###-####

with a copy to (which shall not constitute notice):

Olshan Frome Wolosky LLP

Park Avenue Tower

65 East 55th Street

New York, New York 10022

Fax: (212)  ###-###-####

Attention: Steven Wolosky

                 Andrew Freedman

This Agreement shall be governed by and construed and enforced in accordance with the laws of the State of Delaware without reference to the conflict of laws principles thereof. Each of the Parties hereto irrevocably agrees that any legal action or proceeding with respect to this Agreement and the rights and obligations arising hereunder, or for recognition and enforcement of any judgment in respect of this Agreement and the rights and obligations arising hereunder brought by the other party hereto or its successors or assigns, shall be brought and determined exclusively in the Delaware Court of Chancery and any state appellate court therefrom within the State of Delaware (or, if the Delaware Court of Chancery declines to accept jurisdiction over a particular matter, any state or federal court within the State of Delaware). Each of the Parties hereto hereby irrevocably submits with regard to any such action or proceeding for itself and in respect of its property, generally and unconditionally, to the personal jurisdiction of the aforesaid courts and agrees that it will not bring any action relating to this Agreement in any court other than the aforesaid courts. Each of the Parties hereto hereby irrevocably waives, and agrees not to assert in any action or proceeding with respect to this Agreement, (a) any claim that it is not personally subject to the jurisdiction of the above-named courts for any reason, (b) any claim that it or its property is exempt or immune from jurisdiction of any such court or from any legal process commenced in such courts (whether through service of notice, attachment prior to judgment, attachment in aid of execution of judgment, execution of judgment or otherwise) and (c) to the fullest extent permitted by applicable legal requirements, any claim that (i) the suit, action or proceeding in such court is brought in an inconvenient forum, (ii) the venue of such suit, action or proceeding is improper or (iii) this Agreement, or the subject matter hereof, may not be enforced in or by such courts.

This Agreement may be executed in two or more counterparts which together shall constitute a single agreement.

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This Agreement contains the entire understanding of the Parties hereto with respect to its subject matter. There are no restrictions, agreements, promises, representations, warranties, covenants or undertakings between the Parties other than those expressly set forth herein. No modifications of this Agreement can be made except in writing signed by an authorized representative of each the Company and Starboard. No failure on the part of any Party to exercise, and no delay in exercising, any right, power or remedy hereunder shall operate as a waiver thereof, nor shall any single or partial exercise of such right, power or remedy by such Party preclude any other or further exercise thereof or the exercise of any other right, power or remedy. All remedies hereunder are cumulative and are not exclusive of any other remedies provided by law. The terms and conditions of this Agreement shall be binding upon, inure to the benefit of, and be enforceable by the Parties hereto and their respective successors, heirs, executors, legal representatives, and permitted assigns. No Party shall assign this Agreement or any rights or obligations hereunder without, with respect to any member of Starboard, the prior written consent of the Company, and with respect to the Company, the prior written consent of Starboard. This Agreement is solely for the benefit of the Parties hereto and is not enforceable by any other persons.

(a) Each of the Parties covenants and agrees that, for so long as either of the New Appointees or their respective Replacement Director(s) is serving as a member of the Board, neither it nor any of its respective agents, subsidiaries, Affiliates, successors, assigns, officers, key employees or directors and with respect to Starboard its New Appointees and Replacement Directors, shall in any way disparage, call into disrepute, or otherwise defame or slander the other Parties or such other Parties’ subsidiaries, Affiliates, successors, assigns, officers (including any current officer of a Party or a Parties’ subsidiaries who no longer serves in such capacity following the execution of this Agreement), directors (including any current director of a Party or a Parties’ subsidiaries who no longer serves in such capacity following the execution of this Agreement), employees, stockholders, agents, attorneys or representatives, or any of their products or services, in any manner that would damage the business or reputation of such other Parties, their products or services or their subsidiaries, Affiliates, successors, assigns, officers (or former officers), directors (or former directors), employees, stockholders, agents, attorneys or representatives.

(b) Starboard hereby agrees for the benefit of the Company, and each controlling person, officer, director, stockholder, agent, Affiliate, employee, partner, attorney, heir, assign, executor, administrator, predecessor and successor, past and present, of the Company (the Company and each such person being a “Company Released Person”) as follows:

(i) Starboard, for themselves and for their members, officers, directors, assigns, agents and successors, past and present, hereby agrees and confirms that, effective from and after the date of this Agreement, they hereby acknowledge full and complete satisfaction of, and covenant not to sue, and forever fully release and discharge each Company Released Person of, and hold each Company Released Person harmless from,

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any and all rights, claims, warranties, demands, debts, obligations, liabilities, costs, attorneys’ fees, expenses, suits, losses and causes of action of any nature whatsoever, whether known or unknown, suspected or unsuspected (collectively, “Claims”) that Starboard may have against the Company Released Persons, in each case with respect to events occurring prior to the date of the execution of this Agreement.

(ii) Starboard understands and agrees that the Claims released by Starboard above include not only those Claims presently known but also include all unknown or unanticipated claims, rights, demands, actions, obligations, liabilities, and causes of action of every kind and character that would otherwise come within the scope of the Claims as described above. Starboard understands that they may hereafter discover facts different from or in addition to what they now believe to be true, which if known, could have materially affected this release of Claims, but they nevertheless waive any claims or rights based on different or additional facts.

(c) Starboard agrees that, during the term of the Agreement, (i) Starboard shall not, without the consent of the Company, instigate, solicit, assist, intervene in, or otherwise voluntarily participate in any litigation or arbitration in which the Company or any of its officers or directors are named as parties; provided that the foregoing shall not prevent Starboard from responding to a validly issued legal process and (ii) Starboard agrees to give the Company at least five (5) business days’ notice of the receipt of any legal process requesting information regarding the Company or any of its officers or directors, to the extent that such notice is legally permissible.

(d) The Company hereby agrees for the benefit of Starboard, and each controlling person, officer, director, stockholder, agent, Affiliate, employee, partner, attorney, heir, assign, executor, administrator, predecessor and successor, past and present, thereof, as well as each New Nominee (Starboard and each such person being a “Starboard Released Person”) as follows:

(i) the Company, for itself and for its Affiliates, officers, directors, assigns, agents and successors, past and present, hereby agrees and confirms that, effective from and after the date of this Agreement, it hereby acknowledges full and complete satisfaction of, and covenants not to sue, and forever fully releases and discharges each Starboard Released Person of, and holds each Starboard Released Person harmless from, any and all Claims of any nature whatsoever, whether known or unknown, suspected or unsuspected, that the Company may have against the Starboard Released Persons, in each case with respect to events occurring prior to the date of the execution of this Agreement.

(ii) the Company understands and agrees that the Claims released by the Company above include not only those Claims presently known but also include all unknown or unanticipated claims, rights, demands, actions, obligations, liabilities, and causes of action of every kind and character that would otherwise come within the scope of the Claims as described above. The Company understands that it may hereafter discover facts different from or in addition to what it now believes to be true, which if known, could have materially affected this release of Claims, but it nevertheless waives any claims or rights based on different or additional facts.

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(e) The Parties intend that the foregoing releases be broad with respect to the matter(s) released; provided however, any release of Claims shall not include claims to enforce the terms of this Agreement and; provided further that nothing in the foregoing shall be deemed or construed, now or hereafter, as limiting in any manner any right of indemnification inuring to the benefit of any director or former director of the Company arising under the organization documents of the Company or otherwise.

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IN WITNESS WHEREOF, this Agreement has been duly executed and delivered by the duly authorized signatories of the Parties as of the date hereof.

INTEGRATED DEVICE TECHNOLOGY, INC.

STARBOARD

EXHIBIT A

Starboard

STARBOARD VALUE AND OPPORTUNITY MASTER FUND LTD

STARBOARD VALUE AND OPPORTUNITY S LLC

STARBOARD VALUE LP

STARBOARD VALUE GP LLC

STARBOARD PRINCIPAL CO LP

STARBOARD PRINCIPAL CO GP LLC

JEFFREY C. SMITH

MARK MITCHELL

PETER A. FELD

EXHIBIT B