Exhibit 10.2

INCREMENTAL COMMITMENT AGREEMENT

NORDEA BANK FINLAND PLC, NEW YORK BRANCH

437 Madison Avenue, 21st Floor

New York, New York 10022

July 25, 2013

Atwood Offshore Worldwide Limited

c/o 15835 Park Ten Place Drive

Houston, Texas 77084

Attention: Mark Mey

Tel. No.: (281) 749-7800

Fax No.: (281) 749-8203

re Incremental Commitment

Ladies and Gentlemen:

Reference is hereby made to that certain Credit Agreement, dated as of May 6, 2011, as amended as of November 23, 2011, as further amended on January 18, 2012 and as further amended on August 24, 2012, among Atwood Oceanics, Inc., a Texas corporation (the “Parent”), Atwood Offshore Worldwide Limited, a company formed under the laws of the Cayman Islands (the “Borrower”), the lenders from time to time party thereto (the “Lenders”) and Nordea Bank Finland plc, New York Branch, as Administrative Agent (in such capacity, the “Administrative Agent”) (as may be further amended, restated, amended and restated, supplemented or otherwise modified from time to time, the “Credit Agreement”). Unless otherwise defined herein, capitalized terms used herein shall have the respective meanings set forth in the Credit Agreement.

Each Lender (each a “2013 Incremental Lender”) party to this letter agreement (this “Agreement”) hereby severally agrees to provide the Incremental Commitment(s) set forth opposite its name on Annex I attached hereto (for each such Incremental Lender, its “2013 Incremental Commitment”) under an incremental revolving facility pursuant to Section 2.13 of the Credit Agreement (the “2013 Incremental Facility”). Each 2013 Incremental Commitment provided pursuant to this Agreement shall be subject to the terms and conditions set forth in the Credit Agreement, including Section 2.13 thereof; provided that (i) the “Applicable Margin” with respect to the 2013 Incremental Facility shall be equal to a percentage per annum determined in accordance with the pricing grid (the “Pricing Grid”) set forth on Annex II attached hereto based on the applicable corporate (or corporate family) ratings in respect of the Parent set forth in the Pricing Grid from each of Moody’s Investor Service, Inc. (“Moody’s”) and Standard & Poor’s Ratings Group (“S&P” and, together with Moody’s, collectively, the “Ratings Agencies”) and (ii) notwithstanding anything to the contrary contained in the Credit Agreement,

the “Commitment Commission” under the Credit Agreement with respect to the 2013 Incremental Facility shall be computed at a rate per annum equal to 0.50% multiplied by the unutilized 2013 Incremental Commitment of any Non-Defaulting Lender with a 2013 Incremental Commitment as in effect from time to time.

Each 2013 Incremental Lender acknowledges and agrees that the 2013 Incremental Commitments provided pursuant to this Agreement, in the aggregate amount as set forth on Annex I hereto, shall constitute Incremental Commitments (as specified in said Annex I) under, and as defined in, the Credit Agreement. Each 2013 Incremental Lender further agrees that, with respect to the 2013 Incremental Commitments provided by it pursuant to this Agreement, such 2013 Incremental Lender shall receive an upfront fee as set forth in the letter agreement dated as of July 22, 2013 between the Parent, the Borrower and the Administrative Agent (the “Fee Letter”).

Each 2013 Incremental Lender party to this Agreement (i) confirms that it has received a copy of the Credit Agreement and the other Credit Documents, together with copies of the financial statements referred to therein and such other documents and information as it has deemed appropriate to make its own credit analysis and decision to enter into this Agreement and to become a Lender under the Credit Agreement, (ii) agrees that it will, independently and without reliance upon the Administrative Agent or any other Lender and based on such documents and information as it shall deem appropriate at the time, continue to make its own credit decisions in taking or not taking action under the Credit Agreement, (iii) appoints and authorizes the Administrative Agent, the Collateral Agent and the Security Trustee to take such action as agent on its behalf and to exercise such powers under the Credit Agreement and the other Credit Documents as are delegated to the Administrative Agent, the Collateral Agent and the Security Trustee as the case may be, by the terms thereof, (iv) agrees that it will perform in accordance with their terms all of the obligations which by the terms of the Credit Agreement and the other Credit Documents are required to be performed by it as a Lender, and (v) in the case of each lending institution organized under the laws of a jurisdiction outside the United States, attaches the forms prescribed by the Internal Revenue Service of the United States, certifying as to its entitlement to a complete exemption from United States withholding taxes with respect to all payments to be made under the Credit Agreement and the other Credit Documents. Upon the execution of a counterpart of this Agreement by the Administrative Agent and the Borrower, the delivery to the Administrative Agent of a fully executed copy (including by way of counterparts and by fax) hereof, the payment of any fees (including, without limitation, the fees payable pursuant to the Fee Letter and the upfront fees payable pursuant to the immediately preceding paragraph) required in connection herewith and the satisfaction (or waiver) of the conditions precedent set forth in Annex III attached hereto and the satisfactory completion of KYC in compliance with each Lender’s internal policy, each 2013 Incremental Lender party hereto shall become a Lender pursuant to the Credit Agreement and, to the extent provided in this Agreement, shall have the rights and obligations of a Lender thereunder and under the other Credit Documents.

The Borrower hereby agrees that within thirty days after the date hereof, it shall deliver to the Administrative Agent two appraisal reports as of a recent date from two Approved Appraisers in form and substance reasonably satisfactory to the Administrative Agent stating the then current fair market value of the ATWOOD CONDOR.

You may accept this Agreement by signing the enclosed copies in the space provided below, and returning a counterpart (including by way of facsimile or other electronic transmission) of same to us before the close of business on July, 25, 2013. If you do not so accept this Agreement by such time, your 2013 Incremental Commitments set forth in this Agreement shall be deemed cancelled.

After the execution and delivery to the Administrative Agent of a fully executed copy of this Agreement (including by way of counterparts and by fax) by the parties hereto, this Agreement may only be changed, modified or varied by written instrument in accordance with the requirements for the modification of Credit Documents pursuant to Section 14.12 of the Credit Agreement.

THIS AGREEMENT SHALL BE CONSTRUED IN ACCORDANCE WITH AND GOVERNED BY THE LAW OF THE STATE OF NEW YORK.

Signature Page to Incremental Commitment Agreement

Signature Page to Incremental Commitment Agreement

Signature Page to Incremental Commitment Agreement

Signature Page to Incremental Commitment Agreement

Signature Page to Incremental Commitment Agreement

Signature Page to Incremental Commitment Agreement

Signature Page to Incremental Commitment Agreement

Signature Page to Incremental Commitment Agreement

Signature Page to Incremental Commitment Agreement

Signature Page to Incremental Commitment Agreement

Signature Page to Incremental Commitment Agreement

Signature Page to Incremental Commitment Agreement

ANNEX I

ANNEX II

For purposes of the foregoing, (i) if either Moody’s or S&P shall not have in effect a corporate (or corporate family) rating in respect of the Parent (other than by reason of the circumstances referred to in the last sentence of this definition), then such rating agency shall be deemed to have established a rating in Category 3; (ii) if the ratings established or deemed to have been established by Moody’s and S&P for the Parent shall fall within different Categories, the Applicable Margin shall be based on the higher (the highest category being Category 1) of the two ratings unless one of the two ratings is two or more ratings lower than the other, in which case the Applicable Margin shall be determined by reference to the Category next below that of the higher of the two ratings; and (iii) if the ratings established or deemed to have been established by Moody’s and S&P in respect of the Parent shall be changed (other than as a result of a change in the rating system of Moody’s or S&P), such change shall be effective as of the date on which it is first announced by the applicable rating agency, irrespective of when notice of such change shall have been furnished by the Borrower to the Administrative Agent. Each change in the Applicable Rate shall apply during the period commencing on the effective date of such change and ending on the date immediately preceding the effective date of the next such change. If the rating system of Moody’s or S&P shall change, or if either such rating agency shall cease to be in the business of rating corporate debt obligations, the Borrower and the Lenders shall negotiate in good faith to amend the definition of “Applicable Margin” to reflect such changed rating system or the unavailability of ratings from such rating agency and, pending the effectiveness of any such amendment, the Applicable Margin shall be determined by reference to the rating most recently in effect prior to such change or cessation. The Borrower will furnish to the Administrative Agent promptly after Moody’s or S&P shall have announced a change in the rating established or deemed to have been established, written notice of such rating change.

ANNEX III

The effectiveness of this Agreement shall be subject the satisfaction of the conditions precedent for the incurrence of Incremental Commitments as set forth in Section 2.13 of the Credit Agreement, including, but not limited to the following: