AMENDMENT NO. 1 TO UNIT PURCHASE RIGHTS AGREEMENT

Exhibit 4.1

AMENDMENT NO. 1

TO

UNIT PURCHASE RIGHTS AGREEMENT

This Amendment No. 1 (this “Amendment”), dated as of March 3, 2009, is between Magellan Midstream Partners, L.P., a Delaware limited partnership (the “Partnership”), and Computershare Trust Company, N.A., a federally chartered trust company, as Rights Agent (the “Rights Agent”).

WHEREAS, the Partnership and the Rights Agent entered into a Unit Purchase Rights Agreement, dated as of December 4, 2008 (the “Rights Agreement”);

WHEREAS, the Rights (as defined in the Rights Agreement) are presently redeemable and the Partnership has met all requirements for amendment of the Rights Agreement; and

WHEREAS, the Partnership, pursuant to Section 27 of the Rights Agreement, desires to amend the Rights Agreement as set forth below.

NOW, THEREFORE, the Rights Agreement is hereby amended as follows:

Section 1 of the Rights Agreement is amended by adding thereto the following as Sections 1(w) and 1(x) and existing Sections 1(w) through (z) shall be re-numbered as Sections 1(y) through 1(bb):

(w) “Simplification Agreement” shall mean the Agreement Relating to Simplification of Capital Structure, dated as of March 3, 2009, by and among Magellan Midstream Holdings, L.P., a Delaware limited partnership (“Holdings”), Magellan Midstream Holdings GP, LLC, a Delaware limited liability company (“Holdings GP”), the General Partner, and the Partnership, as the same may be amended from time to time.

(x) “Simplification Documents” shall mean the Fifth Amended and Restated Agreement of Limited Partnership of the Partnership, the Plan of Liquidation, among Holdings and Holdings GP, the Contribution and Assumption Agreement among the Partnership, the General Partner, Holdings, Holdings GP and MGG GP Holdings, LLC, a Delaware limited liability company, a form of each of which is attached as an annex to the Simplification Agreement, and the IDR Entity Assumption Agreement among the

Partnership, Magellan IDR LP, LLC, a Delaware limited liability company and Magellan IDR, L.P., a Delaware limited partnership, and, together with all documents, agreements, certificates or instruments contemplated by or related to such agreements, as said Simplification Documents may be amended from time to time.

The Rights Agreement is amended by adding a Section 37 thereof which shall read as follows:

“Section 37. Exception For Simplification Agreement. Notwithstanding any provision of this Agreement to the contrary, neither a Distribution Date, Triggering Event, Section 13 Event, nor Unit Acquisition Date shall be deemed to have occurred, none of Holdings, Holdings GP or any of their Affiliates or Associates shall be deemed to have become an Acquiring Person, and no holder of any Rights, GP Rights or IDR Rights shall be entitled to exercise such Rights, GP Rights or IDR Rights under, or be entitled to any rights pursuant to, any of Sections 3, 7, 11 or 13 of this Agreement, in any such case by reason of (a) the approval, execution or delivery of the Simplification Agreement, the Simplification Documents, or any amendments thereof or (b) the commencement or, prior to termination of the Simplification Agreement, the consummation of any of the steps and actions contemplated by the Simplification Agreement, or by the Simplification Documents.”

This Amendment shall be deemed effective as of the date hereof as if executed by both parties hereto on such date. Except as amended hereby, the Rights Agreement shall remain in full force and effect and shall be otherwise unaffected hereby.

This Amendment shall be deemed to be a contract made under the laws of the State of Delaware and for all purposes shall be governed by and construed in accordance with the laws of such state applicable to contracts to be made and performed entirely within such state. This Amendment may be executed in any number of counterparts, each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument. If any term, provision, covenant or restriction of this Amendment is held by a court of competent jurisdiction or other authority to be invalid, illegal, or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Amendment shall remain in full force and effect and shall in no way be affected, impaired or invalidated.

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed as of the date set forth above.

SIGNATURE PAGE TO AMENDMENT NO. 1 TO

MAGELLAN MIDSTREAM PARTNERS, L.P. UNIT PURCHASE RIGHTS AGREEMENT