FIRST AMENDMENT TO

Exhibit 10.2

FIRST AMENDMENT

TO

REGISTRATION RIGHTS AGREEMENT

This FIRST AMENDMENT TO REGISTRATION RIGHTS AGREEMENT (this “Amendment”) is made and entered into this 14th day of October, 2009, by and among Magellan Petroleum Corporation, a Delaware corporation (the “Company”), Young Energy Prize S.A., a Luxembourg corporation (“YEP”), and YEP I, SICAV-FIS, a Luxembourg entity (“Fund”). This Amendment amends the Registration Rights Agreement dated as of July 9, 2009 (the “Registration Rights Agreement”) between the Company and YEP. Capitalized terms used but not otherwise defined in this Amendment shall have the meanings given to such terms in the Registration Rights Agreement. The Company, YEP, and Fund are collectively the “Parties” hereunder, and each of them individually is a “Party.”

WHEREAS, pursuant to the Registration Rights Agreement, YEP has the right to require the Company, upon notice and in compliance with the terms and conditions set forth in the Registration Rights Agreement, to prepare and file with the SEC a Registration Statement covering the Registrable Securities;

WHEREAS, the Company and Fund are parties to that certain Purchase and Sale Agreement dated October 14, 2009 (the “NP Purchase Agreement”), pursuant to which the Company shall issue shares of its Common Stock to Fund as partial consideration for its purchase of a membership interest in Nautilus Poplar LLC;

WHEREAS, Fund is an affiliate of YEP;

WHEREAS, the Parties desire to amend the Registration Rights Agreement as set forth herein, including, without limitation, to (i) add Fund as a party thereto, (ii) include the shares of the Company’s Common Stock issuable to Fund pursuant to the NP Purchase Agreement as Registrable Securities; and (iii) set certain limitations on the number of Registration Statements that the Company shall be obligated to file and the Effectiveness Period of each such Registration Statement.

WHEREAS, Section 7(a) of the Registration Rights Agreement provides that the Registration Rights Agreement may be amended only by a writing signed by the Company and YEP.

NOW, THEREFORE, in consideration of the mutual covenants, agreements and for other good and valuable consideration, the receipt and adequacy of which is hereby acknowledged, the Parties hereby agree as follows:

1. Amendment of Registration Rights Agreement.

(a) The following defined terms shall be added to Section 1 of the Registration Rights Agreement:

“NP Purchase Agreement” means that certain Purchase and Sale Agreement dated October 14, 2009 among White Bear LLC, a Montana limited liability company, YEP I, SICAV-FIS, a Luxembourg entity (“Fund”), and the Company.

(b) The definition of “Shares” in Section 1 of the Registration Rights Agreement shall be amended to read in its entirety as follows:

“Shares” shall mean (i) the shares of Common Stock issued to the Investor at the Closing pursuant to the Purchase Agreement, and (ii) the shares of Common Stock issued to Fund pursuant to the NP Purchase Agreement.

(c) The following sentence shall be added at the end of Section 2(a):

“Notwithstanding anything else to the contrary herein, the holders of a majority of the Registrable Securities shall only have the right to require the Company to file, and the Company shall only be obligated to file, three (3) Registration Statements pursuant to this Section 2(a).”

(d) Section 3(a) shall be deleted in its entirety and replaced as follows:

“use commercially reasonable efforts to cause the Registration Statement to become effective after 4:00 E.S.T. (the date the Registration Statement is declared effective shall be referred to as the “Effective Date”) and to remain continuously effective for a period that will terminate upon the earlier of (i) the date on which all Registrable Securities covered by such Registration Statement, as amended from time to time, have been sold, (ii) the date on which all Registrable Securities covered

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by such Registration Statement may be sold without restriction pursuant to Rule 144, or (iii) six (6) months following the Effective Date (the “Effectiveness Period”), and advise the Investors in writing when the Effectiveness Period has expired.”

(e) The following shall be added to the end of Section 6(a):

“or (iv) the failure by the Investor to independently comply with any applicable law or regulation or to take any other action required of a seller of securities by a party in the position of the Investor (including any obligations of an underwriter if the Investor is deemed to be acting as an underwriter).”

(f) The following provisions shall be deleted from Exhibit A (“Plan of Distribution”):

(i) From Paragraph 2:

“short sales effected after the date the registration statement of which this Prospectus is a part declared effective the SEC;”

(ii) From Paragraph 4:

“which may in turn engage in short sales of the common stock in the course of hedging positions they assume. The selling Stockholders may also sell shares of our common stock short and deliver these securities to close out their short positions, or loan or pledge the common stock to broker-dealers that in turn may sell these securities.”

(g) The following shall be added to the end of the last Paragraph in Exhibit A (“Plan of Distribution”):

“or (3) six (6) months following the effective date of the registration statement.”

2. Joinder Agreement of Fund. Fund hereby agrees, effective as of the date of this Amendment, to become a party to the Registration Rights Agreement, as the same is amended by this Amendment, and to be bound by all of the terms and conditions thereunder, which, pursuant to Section 7(d) of the Registration Rights Agreement, shall inure to the benefit of and be binding upon the permitted successors and assigns of Fund. The Parties acknowledge and agree that, for all purposes under the Registration Rights Agreement, Fund shall be included within the term “Investor.” YEP and Fund shall exercise the rights of the Investor under the Registration Rights Agreement in such manner as the holders of a majority in interest of the Registrable Securities shall agree.

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3. Effect of this Amendment. Except as specifically amended as set forth herein, each term and condition of the Registration Rights Agreement shall continue in full force and effect.

4. Counterparts; Facsimile Signatures. This Amendment may be executed or consented to in counterparts, each of which shall be deemed an original and all of which taken together shall constitute one and the same instrument. This Amendment may be executed and delivered by facsimile or electronically and, upon such delivery, the facsimile or electronically transmitted signature will be deemed to have the same effect as if the original signature had been delivered to the other party.

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The parties have caused this Amendment to be duly executed and delivered by their proper and duly authorized officers as of the date and year first written above.

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