ENTERPRISE GP HOLDINGS L.P.

Exhibit 1.2

ENTERPRISE GP HOLDINGS L.P.

1,821,428 Units

Representing Limited Partner Interests

Unit Purchase Agreement

Houston, Texas

August 23, 2005

EPE UNIT L.P.

2727 NORTH LOOP WEST, SUITE 101

HOUSTON, TEXAS 77008-1044

Ladies and Gentlemen:

Enterprise GP Holdings L.P., a limited partnership organized under the laws of Delaware (the “Partnership”), proposes to directly sell (the “Offering”) to EPE Unit L.P., a Delaware limited partnership (the “Employee Partnership”), 1,821,428 units (the “Units”), each representing a limited partner interest in the Partnership (“Partnership Units”). Certain terms used herein are defined in Section 11 hereof, and, in addition, other terms used but not defined herein have the meanings assigned to them in the underwriting agreement (the “Underwriting Agreement”), dated as of even date herewith, by and among the Partnership, EPE Holdings, LLC, a Delaware limited liability company and general partner of the Partnership (the “General Partner,” and together with the Partnership, the “Enterprise Parties”), and the underwriters named therein (the “Underwriters”), relating to the Partnership’s proposed sale of an aggregate 10,778,572 units (the “Underwritten Units”), each representing a limited partner interest in the Partnership, to the Underwriters.

This is to confirm the agreement among the Enterprise Parties, and the Employee Partnership concerning the purchase of the Units from the Partnership by the Employee Partnership.

1. Representations and Warranties. Each of the Enterprise Parties jointly and severally represents and warrants to, and agrees with, the Employee Partnership as set forth below in this Section 1.

(a) Registration. The Partnership has prepared and filed with the Commission (as defined herein) a Registration Statement (File No. 333-124320) on Form S-1, including a related preliminary prospectus, for registration under the Act (as defined herein) of the offering and sale of the Units. The Partnership has filed one or more amendments thereto, including a related preliminary prospectus in accordance with Rule 424(b), each

of which has previously been furnished to you. The Partnership has included in such Registration Statement, as amended at the Effective Date, all information (other than Rule 430A Information (as defined herein)) required by the Act and the rules thereunder to be included in such Registration Statement and the Prospectus (as defined herein). The Partnership will file with the Commission a final Prospectus in accordance with Rules 430A and 424(b). As filed, such final Prospectus, shall contain all Rule 430A Information, together with all other such required information, and, except to the extent the Employee Partnership shall agree in writing to a modification, shall be in all substantive respects in the form furnished to the Employee Partnership prior to the Execution Time (as defined herein) or, to the extent not completed at the Execution Time, and, shall contain only such specific additional information and other changes (beyond that contained in the latest Preliminary Prospectus) as the Partnership has advised the Employee Partnership, prior to the Execution Time, will be included or made therein. The Registration Statement has become effective under the Act; no stop order suspending the effectiveness of the Registration Statement or any part thereof is in effect; and no proceedings for such purpose are pending before or, to the knowledge of the Enterprise Parties, threatened by the Commission.

(b) No Material Misstatements or Omissions. On the Effective Date, the Registration Statement did or will, and when the Prospectus is first filed (if required) in accordance with Rule 424(b) and on the Closing Date (as defined herein), the Prospectus (and any supplements thereto) will, conform in all material respects to the applicable requirements of the Act and the rules and regulations thereunder; on the Effective Date, the Registration Statement did not or will not contain an untrue statement of a material fact or omit to state a material fact required to be stated therein or necessary in order to make the statements therein not misleading; and, on the Effective Date, the Prospectus, if not filed pursuant to Rule 424(b), will not, and on the date of any filing pursuant to Rule 424(b) and on the Closing Date, the Prospectus (together with any supplement thereto) will not, include any untrue statement of a material fact or omit to state a material fact necessary in order to make the statements therein, in the light of the circumstances under which they were made, not misleading; and each of the statements made by the Partnership in the Registration Statement, and to be made in the Prospectus and any further amendments or supplements to the Registration Statement or Prospectus within the coverage of Rule 175(b) of the rules and regulations under the Act, including (but not limited to) any statements with respect to estimated available cash, future cash distributions of the Partnership and any statements made in support thereof or related thereto under “Our Cash Distribution Policy and Restrictions on Distributions” or the anticipated ratio of taxable income to distributions was made or will be made with a reasonable basis and in good faith.

(c) Formation and Qualification of the Enterprise Parties. Each of the Enterprise Parties has been duly formed and is validly existing in good standing under the laws of the State of Delaware with all limited liability company or limited partnership, as the case may be, power and authority necessary to own or hold its properties and conduct the businesses in which it is engaged and, (i) in the case of the General Partner, to act as general partner of the Partnership, and (ii) in the case of the General Partner and the Partnership to execute and deliver this Agreement and to consummate the transactions

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contemplated hereby. Each of the General Partner and the Partnership is duly registered or qualified to do business and is in good standing as a foreign limited liability company or limited partnership, as the case may be, in each jurisdiction in which its ownership or lease of property or the conduct of its businesses requires such qualification or registration, except where the failure to so qualify or register would not, (i) individually or in the aggregate, have a material adverse effect on the condition (financial or otherwise), results of operations, business or prospects of the Enterprise Parties, taken as a whole (an “EPE Material Adverse Effect”) or (ii) subject the limited partners of the Partnership to any material liability or disability.

(d) Valid Issuance of the Units. The Units and the limited partner interests represented thereby, will be duly authorized in accordance with the Partnership Agreement and, when issued and delivered to the Employee Partnership against payment therefor in accordance with the terms hereof, will be validly issued, fully paid (to the extent required under the Partnership Agreement) and nonassessable (except as such nonassessability may be affected by (i) matters described in the Prospectus under the captions “Risk Factors—Your liability as a limited partner may not be limited, and our unitholders may have to repay distributions or make additional contributions to us under certain circumstances” and “Description of Our Partnership Agreement—Limited Liability” and (ii) Sections 17-303 and 17-607 of the Delaware LP Act).

(e) Authority. Each of the Enterprise Parties has all requisite limited liability company and limited partnership power and authority, as the case may be, to execute and deliver this Agreement and perform its respective obligations hereunder. The Partnership has all requisite power and authority to issue, sell and deliver the Units, in accordance with and upon the terms and conditions set forth in this Agreement, the Partnership Agreement, the Registration Statement and the Prospectus.

(f) Authorization, Execution and Delivery of Agreements.

(i) This Agreement has been duly authorized, validly executed and delivered by each of the Enterprise Parties.

(ii) The Partnership Agreement will be duly authorized, executed and delivered by the General Partner and will be a valid and legally binding agreement of the General Partner, enforceable against the General Partner in accordance with its terms; and

(iii) The GP LLC Agreement will be duly authorized, executed and delivered by Dan Duncan LLC, a Texas limited liability company (“DD LLC”), and will be a valid and legally binding agreement of DD LLC, enforceable against DD LLC in accordance with its terms; and

except, with respect to each agreement described in this Section, as the enforceability thereof may be limited by bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and other similar laws relating to or affecting creditors’ rights generally and by general principles of equity (regardless of whether such enforceability is considered in a proceeding in equity or at law).

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(g) No Conflicts. None of the (i) offering, issuance and sale by the Partnership of the Units, (ii) the execution, delivery and performance of this Agreement by the Enterprise Parties, or (iii) consummation of the transactions contemplated hereby (A) conflicts or will conflict with or constitutes or will constitute a violation of any organizational documents of any of the Enterprise Parties, (B) conflicts or will conflict with or constitutes or will constitute a breach or violation of, or a default (or an event that, with notice or lapse of time or both, would constitute such a default) under, any indenture, mortgage, deed of trust, loan agreement, lease or other agreement or instrument to which any of the Enterprise Parties is a party or by which any of them or any of their respective properties may be bound, (C) violates or will violate any statute, law or regulation or any order, judgment, decree or injunction of any court, arbitrator or governmental agency or body having jurisdiction over any of the Enterprise Parties, or any of their properties or assets, or (D) results or will result in the creation or imposition of any lien, charge or encumbrance upon any property or assets of any of the Enterprise Parties, other than Liens in favor of lenders under the Credit Facility or the EPCO Holdings Credit Facility, which conflicts, breaches, violations, defaults or liens, in the case of clauses (B) or (D), would, individually or in the aggregate, have an EPE Material Adverse Effect.

(h) Investment Company/Public Utility Holding Company. None of the Enterprise Parties is now, or after the sale of the Units to be sold by the Partnership hereunder and application of the net proceeds from such sale as described in the Prospectus under the caption “Use of Proceeds” will be, (i) an “investment company” or a company “controlled by” an “investment company” within the meaning of the Investment Company Act of 1940, as amended (the “Investment Company Act”), or (ii) a “holding company” or a “subsidiary company” or “affiliate” of a “holding company” under the Public Utility Holding Company Act of 1935, as amended (the “Public Utility Holding Company Act”).

(i) NYSE Listing. The Units being sold hereunder by the Partnership have been approved for listing on the New York Stock Exchange (the “NYSE”), subject only to official notice of issuance.

(j) Absence of Certain Actions. No action has been taken and no statute, rule, regulation or order has been enacted, adopted or issued by any governmental agency or body which prevents the issuance or sale of the Units in any jurisdiction; no injunction, restraining order or order of any nature by any federal or state court of competent jurisdiction has been issued with respect to any of the Enterprise Parties which would prevent or suspend the issuance or sale of the Units or the use of the Preliminary Prospectus or the Prospectus in any jurisdiction; no action, suit or proceeding is pending against or, to the knowledge of the Enterprise Parties, threatened against or affecting any of the Enterprise Parties before any court or arbitrator or any governmental agency, body or official, domestic or foreign, which could reasonably be expected to interfere with or adversely affect the issuance of the Units or in any manner draw into question the validity

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or enforceability of this Agreement or any action taken or to be taken pursuant hereto; and the Partnership has complied with any and all requests by any securities authority in any jurisdiction for additional information to be included in the Preliminary Prospectus and the Prospectus.

2. Representations of the Employee Partnership.

(a) Formation and Qualification of the Employee Partnership. The Employee Partnership has been duly formed and is validly existing in good standing under the laws of the State of Delaware with all partnership power and authority necessary to own or hold its properties and conduct the businesses in which it is engaged and to execute and deliver this Agreement and consummate the transactions contemplated thereby, in all respects as described in the Registration Statement and the Prospectus. The Employee Partnership is duly registered or qualified to do business and is in good standing as a foreign limited partnership in each jurisdiction in which its ownership or lease of property or the conduct of its businesses requires such qualification or registration, except where the failure to so qualify or register would not, (i) individually or in the aggregate, have a material adverse effect on the condition (financial or otherwise), results of operations, business or prospects of the Employee Partnership (an “Employee Partnership Material Adverse Effect”) or (ii) subject the limited partners of the Employee Partnership to any material liability or disability.

(b) No Conflicts. Neither the execution, delivery and performance of this Agreement by the Employee Partnership nor the consummation of the transactions contemplated hereby (A) conflicts or will conflict with or constitutes or will constitute a violation of the organizational documents of any of the Employee Partnership, (B) conflicts or will conflict with or constitutes or will constitute a breach or violation of, or a default (or an event that, with notice or lapse of time or both, would constitute such a default) under, any indenture, mortgage, deed of trust, loan agreement, lease or other agreement or instrument to which the Employee Partnership is a party or by which it or any of its respective properties may be bound, (C) violates or will violate any statute, law or regulation or any order, judgment, decree or injunction of any court, arbitrator or governmental agency or body having jurisdiction over the Employee Partnership, or any of its properties or assets, or (D) results or will result in the creation or imposition of any lien, charge or encumbrance upon any property or assets of the Employee Partnership, other than Liens in favor of lenders under the Credit Facility or the EPCO Holdings Credit Facility, which conflicts, breaches, violations, defaults or liens, in the case of clauses (B) or (D), would, individually or in the aggregate, have an Employee Partnership Material Adverse Effect.

3. Purchase and Sale. Subject to the terms and conditions and in reliance upon the representations and warranties herein set forth, the Partnership agrees to sell to the Employee Partnership, and the Employee Partnership hereby agrees to purchase from the Partnership, at a purchase price of $28.00 per unit, the Units.

4. Delivery and Payment. Delivery of and payment for the Units shall be made at 10:00 a.m., New York City time, on August, 2005 or at such time on such later date not more

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than three Business Days after the foregoing date as the Employee Partnership shall designate, which date and time may be postponed by agreement between the Employee Partnership and the Partnership (such date and time of delivery and payment for the Units being herein called the “Closing Date”). Delivery of the Units shall be made to the Employee Partnership against payment by the Employee Partnership of the purchase price thereof to or upon the order of the Partnership by wire transfer payable in same-day funds to an account specified by the Partnership. The Partnership shall deliver original unit certificates representing the Units, duly executed by the Partnership, unless the Employee Partnership shall otherwise instruct.

5. Conditions to the Obligations of the Employee Partnership. The obligations of the Employee Partnership to purchase the Units shall be subject to the accuracy of the representations and warranties on the part of the Enterprise Parties contained herein as of the Execution Time and the Closing Date, to the performance by the Enterprise Parties of their obligations hereunder and to the following additional conditions:

(a) If the Registration Statement has not become effective prior to the Execution Time, unless the Employee Partnership agree in writing to a later time, the Registration Statement will become effective not later than (i) 6:00 p.m. New York City time on the date of determination of the public offering price, if such determination occurred at or prior to 3:00 p.m. New York City time on such date or (ii) 9:30 a.m. on the Business Day following the day on which the public offering price was determined, if such determination occurred after 3:00 p.m. New York City time on such date; if filing of the Prospectus, or any supplement thereto, is required pursuant to Rule 424(b), the Prospectus, and any such supplement, will be filed in the manner and within the time period required by Rule 424(b); and no stop order suspending the effectiveness of the Registration Statement or any part thereof shall have been issued and no proceedings for that purpose shall have been instituted or threatened, and all requests of the Commission for inclusion of additional information in the Registration Statement or the Prospectus or otherwise shall have been complied with.

(b) All partnership and limited liability company proceedings and other legal matters incident to the authorization, form and validity of this Agreement, the Units, the Registration Statement, the Preliminary Prospectus and the Prospectus, and all other legal matters relating to this Agreement and the transactions contemplated hereby shall be reasonably satisfactory in all material respects to representatives of the Employee Partnership, and the Partnership shall have furnished to such representatives all documents and information that they may reasonably request to enable them to pass upon such matters.

(c) The NYSE shall have approved the Units for listing, subject only to official notice of issuance.

(d) The closing of the purchase and sale of the Underwritten Units shall have occurred.

If any of the conditions specified in this Section 5 shall not have been fulfilled when and as provided in this Agreement, this Agreement and all obligations of the Employee Partnership

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hereunder may be canceled at, or at any time prior to, the Closing Date by the Employee Partnership. Notice of such cancellation shall be given to the Partnership in writing or by telephone or facsimile confirmed in writing.

6. Notices. All communications hereunder will be in writing and effective only upon receipt, and, if sent to the Employee Partnership, will be mailed, delivered or telefaxed to EPE Unit L.P., 2727 North Loop West, Suite 101, Houston, Texas 77008-1044, Attention: Chief Legal Officer (Fax No.: (713) 803-6570)); or, if sent to the Enterprise Parties, will be mailed, delivered or faxed to Enterprise GP Holdings L.P., 2727 North Loop West, Suite 101, Houston, Texas 77008-1044, Attention: Chief Legal Officer (Fax No.: (713) 803-6570)).

7. Successors. This Agreement will inure to the benefit of and be binding upon the parties hereto and their respective successors and the officers, directors, employees and agents, and no other person will have any right or obligation hereunder.

8. Applicable Law. THIS AGREEMENT WILL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF TEXAS APPLICABLE TO CONTRACTS MADE AND TO BE PERFORMED WITHIN THE STATE OF TEXAS.

9. Counterparts. This Agreement may be signed in one or more counterparts, each of which shall constitute an original and all of which together shall constitute one and the same Agreement.

10. Headings. The section headings used herein are for convenience only and shall not affect the construction hereof.

11. Definitions. The terms which follow, when used in this Agreement, shall have the meanings indicated.

“Act” shall mean the Securities Act of 1933, as amended, and the rules and regulations of the Commission promulgated thereunder.

“Affiliate” has the meaning set forth in Rule 405 promulgated under the Act.

“Business Day” shall mean any day other than a Saturday, a Sunday or a legal holiday or a day on which banking institutions or trust companies are authorized or obligated by law to close in Houston, Texas.

“Commission” shall mean the Securities and Exchange Commission.

“Effective Date” shall mean each date and time that the Registration Statement, any post-effective amendment or amendments thereto and any Rule 462(b) Registration Statement became or become effective.

“Execution Time” shall mean the date and time that this Agreement is executed and delivered by the parties hereto.

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“Preliminary Prospectus” shall mean any preliminary prospectus referred to in paragraph 1(a) above and any preliminary prospectus included in the Registration Statement at the Effective Date that omits Rule 430A Information.

“Prospectus” shall mean the prospectus relating to the Units that is first filed pursuant to Rule 424(b) after the Execution Time or, if no filing pursuant to Rule 424(b) is required, shall mean the form of final prospectus relating to the Units included in the Registration Statement at the Effective Date.

“Registration Statement” shall mean the registration statement referred to in Section 1(a) hereof, including exhibits and financial statements, as amended at the Execution Time and, in the event any post-effective amendment thereto or any Rule 462(b) Registration Statement becomes effective prior to the Closing Date, shall also mean such registration statement as so amended or such Rule 462(b) Registration Statement, as the case may be. Such term shall include any Rule 430A Information deemed to be included therein at the Effective Date as provided by Rule 430A.

“Rule 424”, “Rule 430A” and “Rule 462” refer to such rules promulgated under the Act.

“Rule 430A Information” shall mean information with respect to the Units and the offering thereof permitted to be omitted from the Registration Statement when it becomes effective pursuant to Rule 430A.

“Rule 462(b) Registration Statement” shall mean a registration statement and any amendments thereto filed pursuant to Rule 462(b) relating to the offering covered by the registration statement referred to in Section 1(a) hereof.

[Signature Pages to Follow]

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If the foregoing is in accordance with your understanding of our agreement, please sign and return to us the enclosed duplicate hereof, whereupon this letter and your acceptance shall represent a binding agreement among the Enterprise Parties and the Employee Partnership.

Signature Page to Unit Purchase Agreement of

Enterprise GP Holdings L.P.

The foregoing Agreement is hereby

confirmed and accepted as of the

date first above written.

“Employee Partnership”

Signature Page to Unit Purchase Agreement of

Enterprise GP Holdings L.P.