Share Repurchase Agreement dated November 25, 2018

Exhibit 1.2

KOSMOS ENERGY LTD.

COMMON SHARES, PAR VALUE $0.01 PER SHARE

REPURCHASE AGREEMENT

November 25, 2018

FUNDS AFFILIATED WITH WARBURG PINCUS

Repurchase Agreement

November 25, 2018

FUNDS AFFILIATED WITH WARBURG PINCUS

Ladies and Gentlemen:

Introductory.        Kosmos Energy Ltd., a Bermuda exempted company (“Kosmos”), proposes to repurchase (the “Repurchase”) from the shareholders listed on Schedule A hereto (each, a “Shareholder,” and collectively, “Warburg”) on the Closing Date (as defined below) an amount of common shares of Kosmos, par value $0.01 per share (the “Kosmos Common Shares”), as set forth opposite the name of each Shareholder on Schedule A (collectively, the “Repurchased Shares”) subject to the terms and conditions set forth herein.

Each of Kosmos and Warburg understands that, subject to market and other conditions and in the sole discretion of Warburg, on or before November 28, 2018, Warburg may agree to sell and complete a sale of a number of Kosmos Common Shares, to be determined by Warburg, in a registered public offering pursuant to a registration statement on Form S-3 (file number 333-227084) filed by Kosmos with the Securities and Exchange Commission (the “SEC”) (the “Public Resale Offering”). Each of Kosmos and Warburg also understands that, should Warburg undertake the Public Resale Offering, on or before November 28, 2018, Warburg and Kosmos would enter into an underwriting agreement (the “Underwriting Agreement”) with one or more underwriters in connection with the Public Resale Offering.

Kosmos hereby confirms its agreements with Warburg as follows:

Section 1. Purchase, Sale and Delivery of the Repurchased Shares.

(a)       The Repurchased Shares. Upon the terms and subject to the conditions set forth herein, Kosmos agrees to repurchase from Warburg, and Warburg agrees to sell to Kosmos, the Repurchased Shares at a price per share equal to the Net Offering Price (as defined below), provided, however, that the Net Offering Price shall not exceed $6.00 and the aggregate purchase price payable on the Closing Date for the Repurchased Shares shall not exceed $210,000,000. As used herein, “Net Offering Price” shall equal the public offering price per share of Kosmos Common Shares sold in the Public Resale Offering, less underwriting discounts and commissions per share, as set forth on the cover page to the final prospectus supplement to be filed by Kosmos pursuant to Rule 424(b) under the Securities Act of 1933, as amended.

(b)       The Closing Date. Payment for the Repurchased Shares to be sold by Warburg shall be made to Warburg in Federal or other funds immediately available in New York City against delivery of the Repurchased Shares for the respective account of Kosmos at 9:00 a.m., New York City time on the closing date of the Public Resale Offering, or at such other time and on such other date as Kosmos and Warburg shall

mutually agree (the time and date of such payment are hereinafter referred to as the “Closing Date”).

(c)       Delivery of the Shares. The Repurchased Shares shall be registered in such names and in such denominations as Kosmos shall request in writing not later than one full business day prior to the Closing Date. The Repurchased Shares shall be delivered to Kosmos on the Closing Date for the account of Kosmos.

Section 2. Conditions of the Obligations of Kosmos. The obligations of Warburg to deliver the Repurchased Shares and of Kosmos to repurchase and pay for the Repurchased Shares, in each case as provided, shall be subject to the timely performance by Warburg and Kosmos of each of their respective covenants and other obligations hereunder and shall include the entry by the Parties into the Underwriting Agreement on or before November 28, 2018 and the completion of the Public Resale Offering.

If the conditions specified in this ‎Section 2 are not satisfied when and as required to be satisfied, this Agreement may be terminated by Warburg by notice to Kosmos or by Kosmos by notice to Warburg at any time on or prior to the Closing Date, which termination shall be without liability on the part of any party to any other party, except that Section ‎6 shall at all times be effective and shall survive such termination.

Section 3. Notices. All communications hereunder shall be in writing and shall be mailed, hand delivered or facsimilied and confirmed to the parties hereto as follows:

If to Warburg:

Warburg Pincus LLC

450 Lexington Avenue

New York, NY 10017

If to Kosmos:

c/o Kosmos Energy, LLC

8176 Park Lane, Suite 500

Dallas, TX 75231

Attention: General Counsel

With a copy to:

Byron B. Rooney

450 Lexington Avenue

New York, NY 10017

Attention: Byron B. Rooney, Esq.

Any party hereto may change the address for receipt of communications by giving written notice to the others.

Section 4. Successors. This Agreement will inure to the benefit of and be binding upon the parties hereto, and in each case their respective successors, and no other person will have any right or obligation hereunder. The term “successors” shall not include any purchaser of the Kosmos Common Shares from Warburg merely by reason of such purchase.

Section 5. Partial Unenforceability. The invalidity or unenforceability of any Section, paragraph or provision of this Agreement shall not affect the validity or enforceability of any other Section, paragraph or provision hereof. If any Section, paragraph or provision of this Agreement is for any reason determined to be invalid or unenforceable, there shall be deemed to be made such minor changes (and only such minor changes) as are necessary to make it valid and enforceable.

Section 6. Governing Law Provisions. THIS AGREEMENT SHALL BE GOVERNED BY, AND CONSTRUED AND INTERPRETED IN ACCORDANCE WITH, THE INTERNAL LAWS OF THE STATE OF NEW YORK APPLICABLE TO AGREEMENTS MADE AND TO BE PERFORMED IN THAT STATE.

Section 7. General Provisions. This Agreement may be executed in two or more counterparts, each one of which shall be an original, with the same effect as if the signatures thereto and hereto were upon the same instrument. This Agreement may not be amended or modified unless in writing by all of the parties hereto, and no condition herein (express or implied) may be waived unless waived in writing by each party whom the condition is meant to benefit. The Section headings herein are for the convenience of the parties only and shall not affect the construction or interpretation of this Agreement. If the Repurchase is not consummated on or prior to December 4, 2018, this Agreement shall terminate and Kosmos and Warburg shall each be automatically released from all obligations under this Agreement.

If the foregoing is in accordance with your understanding of our agreement, kindly sign and return to Kosmos the enclosed copies hereof, whereupon this instrument, along with all counterparts hereof, shall become a binding agreement in accordance with its terms.

The foregoing Repurchase Agreement is hereby confirmed and accepted by Warburg as of the date first above written.

SCHEDULE A