Exhibit 10.2

SECOND AMENDMENT

TO

SECURITIES PURCHASE AGREEMENT

This SECOND AMENDMENT TO SECURITIES PURCHASE AGREEMENT (this “Amendment”) is made and entered into this 17 day of February, 2011, by and between Magellan Petroleum Corporation, a Delaware corporation (the “Company”), and Young Energy Prize S.A., a Luxembourg corporation (the “Investor”).

WHEREAS, the Company and the Investor are parties to that certain Securities Purchase Agreement dated as of August 5, 2010, as amended by that certain First Amendment to Securities Purchase Agreement dated February 11, 2011 (together, the “Purchase Agreement”);

WHEREAS, Section 7.4 of the Purchase Agreement provides that no provision of the Purchase Agreement may be amended except in a written instrument signed by the Company and the Investor; and

WHEREAS, the Company and the Investor desire to amend the Purchase Agreement as set forth herein.

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 Company and the Investor hereby agree as follows:

1. Amendment of Purchase Agreement. Section 5.1(e) of the Purchase Agreement shall be amended to read in its entirety as follows:

“(e) Evans Shoal Transaction Status. As of the time of any Closing other than the final Closing at which the last of the Shares are sold to and purchased by the Investor to provide funds for use in the closing of the Evans Shoal Transaction, the progress and status of the Evans Shoal Transaction shall be satisfactory to the Investor, and, in the case of such final Closing, the conditions to the closing of the Evans Shoal Transaction shall have been satisfied or waived. Notwithstanding the foregoing and provided that the Company has not recovered its A$10,000,000 deposit under the provisions of the Deed of Variation, the Investor shall be required to complete the final Closing, on or before June 15,

2011, without regard to the failure of the Evans Shoal Transaction to close and without regard to any failure to satisfy any other condition set forth in this Section 5.1 which non-satisfaction is reasonably attributable to the failure to close the Evans Shoal Transaction;”

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

3. 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.

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.