Exhibit 10.1

STOCK PURCHASE PLAN ENGAGEMENT AGREEMENT

Stock Purchase Plan Engagement Agreement dated as of January 29, 2007 (this “Agreement”) between St. Jude Medical, Inc., a Minnesota corporation (the “Company”), and Banc of America Securities LLC (“Broker”), acting as agent for the Company.

WHEREAS, the Company desires to establish a trading plan (subject to the terms and provisions of this Agreement, the “Plan”) that qualifies for the safe harbors provided by Rule 10b-18 (“Rule 10b-18”) and Rule 10b5-1 (“Rule 10b5-1”) each under the Securities Exchange Act of 1934, as amended (the “Exchange Act”); and

WHEREAS, the Company wishes to engage Broker as its exclusive agent to make purchases of shares of the common stock, par value $0.10, of the Company (the “Securities”) on its behalf under the Plan;

NOW, THEREFORE, in consideration of the foregoing and the mutual covenants, agreements, representations and warranties contained in this Agreement and intending to be legally bound, the parties agree as follows:

The Company hereby engages the Broker as the Company’s exclusive agent to purchase the Securities during the term of this Agreement. Subject to the terms and conditions set forth herein, Broker hereby accepts such appointment and engagement.

A.            Broker is authorized to begin purchasing the Securities as agent for the Company pursuant to the Plan on January 29, 2007, after the execution of this Agreement by both parties, and shall cease purchasing the Securities on the Termination Date (as defined below). The time period beginning on the date purchases are to first be made to the date of the termination of the Plan is referred to herein as the “Plan Period”.

B.             (i)          On each Trading Day during the Plan Period on which no Market Disruption Event (as defined below) occurs, Broker shall purchase as agent for the Company and for the account of the Company the lesser of (a) the maximum number of Securities that the Company could purchase under Rule 10b-18 and (b) number of Securities that Broker is able, subject to market conditions and principles of best execution, to purchase as agent for the Company and for the account of the Company on such Trading Day using commercially reasonable means in accordance with the guidelines set forth below (the “Guidelines”). The dollar value of the Securities purchased pursuant to this Plan including commissions, shall not exceed $700,000,000.00.

The Company shall pay to Broker a commission of $0.02 per Security so purchased.

(ii)           A “Trading Day” is any day during the Plan Period that the New York Stock Exchange, Inc. (the “Principal Market”) is open for business and the Securities trade regular way on the Principal Market. “Market Disruption Event” has the meaning set forth in Section 6.3(a) of the 2002 Equity Derivatives Definitions, as published by the International Swaps and Derivatives Association, Inc., and references therein to “Exchange” shall be deemed to be references to the Principal Market.

(iii)          Any Securities so purchased shall be purchased under ordinary principles of best execution at the then-prevailing market price. Subject to the terms set forth in this Agreement, Broker shall have full discretion with respect to the execution of all purchases, and the Company acknowledges and agrees that the Company does not have, and shall not attempt to exercise, any influence over how, when or whether to effect such purchases of Securities pursuant to the Plan. The Company acknowledges and agrees that, in acting under this Agreement, Broker will be an independent contractor and will not be acting as the Company’s trustee or fiduciary or in any similar capacity.

(iv)          In the event that Broker, in its discretion, determines that it is appropriate with regard to any legal, regulatory or self-regulatory requirements or related policies and procedures (whether or not such requirements, policies or

procedures are imposed by law or have been voluntarily adopted by Broker, and including without limitation Rule 10b-18, Rule 10b-5, Regulation 13D-G and Regulation 14E under the Exchange Act, “Requirements”) for Broker to refrain from purchasing Securities or to purchase fewer than the otherwise applicable Number of Shares to be Purchased on any Trading Day during the Plan Period, then Broker may, in its discretion, elect that the Number of Shares to be Purchased for such Trading Day shall be reduced for such day to an amount determined by Broker in its discretion as appropriate with regard to any Requirements.

(v)           Any Number of Shares to be Purchased (and the corresponding purchase price limits or ranges) set forth in the Guidelines shall be adjusted automatically on a proportionate basis to take into account any stock split, reverse stock split or stock dividend with respect to the Securities or any change in capitalization with respect to the Company or any similar event that occurs during the Plan Period, as determined by Broker in good faith and a commercially reasonable manner.

C.            Broker may purchase Securities on the Principal Market, any national securities exchange, in the over-the-counter market, on an automated trading system or otherwise.

D.            Broker shall use good faith efforts to execute all purchase transactions under this Agreement in accordance with the timing, price and volume restrictions contained in subparagraphs (2), (3) and (4) of Rule 10b-18. Nothing herein shall preclude the purchase by Broker of the Securities for its own account, or the solicitation or execution of purchase or sale orders of the Securities for the account of Broker’s clients. Please be advised that, due to the manual process involved in executing and reporting trades on the floor of the New York Stock Exchange, Inc. (the “NYSE”), a trade that is otherwise compliant with the price restrictions of Rule 10b-18 may appear to have been effected outside of the price restriction. Such a condition typically occurs as a result of the delays inherent in the NYSE specialist process of reporting a trade to the Consolidated Tape. In those instances in which there is a delay between the execution and reporting of a trade by the specialist on the NYSE floor, a trade reported to the Consolidated Tape by another market may cause the NYSE trade report to appear as an “uptick”, i.e., a trade executed at a price higher than the highest independent bid or last sale price. These conditions are more likely to occur in actively traded stocks.

E.            It is the intent of the parties that this Agreement and the Plan comply with the requirements of Rule 10b5-1(c)(1)(i)(B) of the Exchange Act, and the parties agree that this Agreement shall be interpreted to comply with the requirements of Rule 10b5-1(c) and the Company shall take no action that results in this transaction not so complying with such requirements.   

F.             The Company also acknowledges and agrees that any amendment, modification or waiver of this Agreement or the Plan, must be effected in accordance with the requirements for the amendment of a “plan” as defined in Rule 10b5-1(c). Without limiting the generality of the foregoing, any such amendment, modification or waiver shall be made in good faith and not as part of a plan or scheme to evade the prohibitions of Rule 10b-5 under the Exchange Act, and no such amendment, modification or waiver shall be made at any time at which the Company is aware of any material nonpublic information concerning the Company or the Securities. Upon any amendment, modification or waiver of this Agreement or the Plan, the Company shall immediately deliver to Broker a letter substantially in the form of Exhibit A hereto.

A.            The Company is not entering this Agreement “on the basis of” (as defined in Rule 10b5-1(b) under the Exchange Act) any material nonpublic information concerning the Securities or the business, operations or prospects of the Company.

B.            During the Plan Period, the Company agrees not to enter into or alter any corresponding or hedging transaction or position with respect to the securities covered by the Plan (including, without limitation, with respect to any securities convertible or exchangeable into the Securities) and agrees not to alter or deviate from the terms of the Plan.

C.            The Company agrees that, during the Plan Period, neither the Company nor its officers or employees shall, directly or indirectly, communicate any information relating to the Securities or the Company to any employee of Broker or its affiliates involved in trading the Securities in connection with the transactions contemplated hereby, who currently include the individuals specified in Annex A hereto.

D.            The execution and delivery of this Agreement and the consummation of the transactions herein contemplated will not (i) result in a breach of any of the terms or provisions of, or constitute a default under, any agreement or instrument to which the Company or any of its subsidiaries is a party or by which the Company or any of its

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subsidiaries is bound, nor will such action result in any violation of the provisions of the certificate of incorporation, by-laws or other constitutive documents of the Company or any statute or any order, rule or regulation of any court or governmental agency or body having jurisdiction over the Company or any of its subsidiaries or any of their respective properties or (ii) conflict with or exceed the authority granted under resolutions of the board of directors of the Company authorizing this Agreement or the consummation of the Plan.

E.            The Company has made, and shall use its best efforts during the Plan Period to make in a timely manner, all filings required to be made by it with the Securities and Exchange Commission, any securities exchange or any other regulatory body with respect to the transactions contemplated hereby. The Company agrees to immediately notify Broker of any failure or delay in making any such filings when due.

F.             Without the prior written consent of Broker, the Company agrees that during the Plan Period (or until the Plan has been terminated, if earlier) the Company shall not, directly or indirectly (including, without limitation, by means of a cash-settled or other derivative instrument) purchase, offer to purchase, place any bid or limit order that would effect a purchase of, any Securities (or an equivalent interest, including a unit of beneficial interest in a trust or limited partnership or a depository share) or any security convertible into or exchangeable for Securities, except for any Securities tendered to or withheld by the Company to satisfy the exercise price of any stock option or to satisfy tax withholding obligations upon the exercise of any stock option or the vesting of any restricted stock under the Company’s stock plans.

G.            The Company shall notify Broker prior to the opening of trading in the Securities on any day on which the Company makes, or expects to be made, any public announcement (as defined in Rule 165(f) under the Securities Act) of any merger, acquisition, or similar transaction involving a recapitalization relating to the Company (other than any such transaction in which the consideration consists solely of cash and there is no valuation period), and shall promptly notify Broker with information relating to actual purchases by the Company during the three calendar months preceding such announcement (unless Broker already has such information relating to actual purchases by the Company). The Company acknowledges that if the Company does not provide such notice and information to Broker, Broker may in it is discretion cease any purchase activity hereunder after such an announcement is made by the Company until such time as the Company provides Broker with the necessary information.

H.            The Company shall, on the business day prior to the intended date of such purchase, notify Broker of the intention on the part of any affiliated purchaser, as defined in Rule 10b-18, of the Company to purchase Securities on any day if such purchase is to be effected otherwise than through Broker pursuant to this Agreement and Broker shall refrain from purchasing any Securities hereunder on the day following receipt of such notice. The Company shall be solely responsible for any purchases made by Broker as the Company’s agent prior to Broker’s receipt of such written notice. Notwithstanding the foregoing, if Broker receives such notice, Broker may nevertheless be entitled to make, and the Company shall be solely responsible for, a purchase hereunder pursuant to a bid made before such notice is received by Broker. The Company shall be solely responsible for notifying Broker of any purchases of Securities by any such affiliated purchaser, and the Company agrees to indemnify and hold harmless Broker for any failure to so notify Broker or any error in any such notification. The Company also acknowledges that purchases of Securities by any such affiliated purchaser (including without limitation any purchases caused or influenced by any action of the Company) may cause the Number of Shares to be Purchased on any Trading Day to be reduced pursuant to Section 2.B(iv) above. The Company acknowledges that any action it takes that causes or influences any purchase of Securities by any affiliated purchaser must comply with the standards set forth in Section 2.F above.

I.              The Company agrees that neither the Company nor any of its affiliates or agents shall take any action that would cause Regulation M under the Exchange Act (“Regulation M”) to be applicable to any purchases of Securities, or any security for which the Securities are a reference security (as defined in Regulation M), by the Company or any of its affiliated purchasers (as defined in Regulation M) during the Plan Period.

J.             The Company represents and warrants that it has publicly disclosed on January 25, 2007 its intention to institute a program for the acquisition of the Securities as contemplated hereby.

K.            The Company acknowledges and agrees that it is not relying, and has not relied, upon Broker or any affiliate of Broker with respect to the legal, accounting, tax or other implications of this Agreement and that it has conducted its own analyses of the legal, accounting, tax and other implications hereof. The Company further acknowledges and agrees that neither Broker nor any affiliate of Broker has acted as its advisor in any capacity in connection with this Agreement or the transactions contemplated hereby. The Company is entering into this Agreement with a full understanding of all of the terms and risks hereof (economic and otherwise), has adequate expertise in financial matters to evaluate those terms and risks and is capable of assuming (financially and otherwise) those risks.

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A.            This Agreement and the Plan shall terminate on the Termination Date. “Termination Date” means the earliest to occur of (i) the close of business on February 28, 2007, (ii) the close of business on the date that the Number of Shares to be Purchased have been purchased, (iii) any Optional Termination Date (as defined below), (iv) the date on which any Required Termination Notice (as defined below) is received by Broker, (v) the date that the Company or any other person publicly announces a tender or exchange offer with respect to the Securities or a merger, acquisition, reorganization, recapitalization or comparable transaction affecting the Securities as a result of which the Securities are to be exchanged or converted into shares of another company and (vi) the date that Broker becomes aware of the commencement or impending commencement of any proceedings in respect of or triggered by the Company’s bankruptcy or insolvency.

B.            This Agreement may be terminated by either party hereto on written notice to the other party in accordance with Section 5.D. below (the date of any such termination, an “Optional Termination Date”).

C.            If, at any time during the Plan Period, any legal or regulatory restriction that is applicable to the Company or the Company’s affiliates would prohibit any purchase pursuant to the Plan, the Company agrees to give Broker notice of such restriction in accordance with clause (i) of Section 5.D below as soon as practicable (such notice, a “Required Termination Notice”). Such notice shall indicate the anticipated duration of the restriction, but shall not include any other information about the nature of the restriction or its applicability to the Company or otherwise communicate any material nonpublic information about the Company or the Securities to Broker.

D.            Notwithstanding the termination of this Agreement, the Company shall be solely responsible for any purchases made by Broker on the Company’s behalf prior to Broker’s receipt of any notice of termination, and if Broker receives such notice, Broker may nevertheless be entitled to make, and the Company shall be solely responsible for, a purchase hereunder pursuant to a bid made before such notice is received by Broker.

A.          Payment for the purchase price of Securities purchased under the Plan for the account of the Company, plus applicable commission, will be delivered to Broker’s account, which Broker shall specify in writing to the Company from time to time, on a normal three-day settlement basis. Broker shall give the Company at least 30 days prior notice before changing such account.

B.            The parties hereto agree and acknowledge that Broker is a “stockbroker” within the meaning of Section 101(53A) of Title 11 of the United States Code (the “Bankruptcy Code”). The parties hereto further agree and acknowledge that this Agreement is a “securities contract,” as such term is defined in Section 741(7) of the Bankruptcy Code, and Broker is entitled to the protections afforded by, among other Sections, Sections 362(b)(6), 546(e) and 555 of the Bankruptcy Code.

C.            This Agreement constitutes the entire agreement between the parties with respect to the Plan and supercedes any prior agreements or understandings with regard to the Plan.

D.            All notices to Broker under this Agreement shall be given to Broker, ATTN: Chip Gibbs, by (i) facsimile at ###-###-#### followed by telephonic confirmation at ###-###-#### or (ii) by certified mail or overnight courier to the address below:

Banc of America Securities LLC

ATTN: Chip Gibbs

9 W. 57^th Street

40^th Floor

New York, NY 10019

All notices to the Company under this Agreement shall be given to Company, ATTN: John C. Heinmiller, in the manner specified by this Agreement by (i) facsimile at ###-###-#### followed by telephonic confirmation at ###-###-#### or (ii) by certified mail or overnight courier to the address below:

St. Jude Medical, Inc.

One Lillehei Plaza

ATTN: John C. Heinmiller

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E.            The Company’s rights and obligations under this Agreement may not be assigned or delegated without the written consent of Broker, and Broker’s rights and obligations under this Agreement may not be assigned or delegated without written consent of the Company.

F.            If any provision of this Agreement is or becomes inconsistent with any applicable present or future law, rule or regulation, that provision will be deemed modified or, if necessary, rescinded in order to comply with the relevant law, rule or regulation. All other provisions of this Agreement will continue and remain in full force and effect.

G.            THIS AGREEMENT SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE INTERNAL LAWS OF THE STATE OF NEW YORK. The parties hereto irrevocably submit to the non-exclusive jurisdiction of the Federal and state courts located in the Borough of Manhattan, in the City of New York in any suit or proceeding arising out of or relating to this Agreement or the transactions contemplated hereby.

H.            EACH PARTY HEREBY IRREVOCABLY WAIVES ANY AND ALL RIGHTS TO TRIAL BY JURY WITH RESPECT TO ANY LEGAL PROCEEDING ARISING OUT OF OR RELATING TO THIS AGREEMENT OR ANY TRANSACTION CONTEMPLATED HEREBY.

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IN WITNESS WHEREOF, the undersigned have signed this Agreement as of the date first written above.

ANNEX A

The Company agrees that, during the Plan Period, neither the Company nor its officers or employees shall, directly or indirectly, communicate any information relating to the Securities or the Company to any employee of Broker or its affiliates involved in trading the Securities in connection with the transactions contemplated hereby, who currently include the following individuals: Dmitry S. Genkin, Sean W. Groenewald, Soo-Il Lee, Anthony P. Paquette, Marc Mezzadri and John Wall, and such other employees as may be identified to the Company in writing by Broker from time to time.

Annex A-1

EXHIBIT A

[Company Letterhead]

[Date]

Banc of America Securities LLC

9 West 57^th Street

New York, NY 10019

Attn: Chip Gibbs

Ladies and Gentlemen:

Reference is made to the Stock Purchase Plan Engagement Agreement (the “Repurchase Agreement”) dated as of [_________] between St. Jude Medical, Inc. (the “Company”) and Banc of America Securities LLC (“Broker”).

In connection with the [amendment/modification/waiver] of the Repurchase Agreement, the Company hereby represents and warrants to Broker that on the date hereof the Company is not aware of any material nonpublic information regarding the Company, and that its decision to [amend/modify/seek a waiver of] the Repurchase Agreement was made in good faith and not as a part of a plan or scheme to evade the prohibitions of Rule 10b-5 under the Securities Exchange Act of 1934, as amended.

Exhibit A-1