Exhibit 99.1

February 14, 2018

TO THE SHAREHOLDERS OF OCEAN RIG UDW INC.:

Enclosed is a Notice of the 2018 Annual General Meeting of Shareholders (the "Meeting") of Ocean Rig UDW Inc. (the "Company"), which will be held at 3^rd Floor, Flagship Building, Harbour Drive, Grand Cayman, Cayman Islands on Monday, March 5, 2018 at 9:00am, local time, and related materials. The Notice of the 2018 Annual General Meeting of Shareholders and related materials can also be found at http://ocean-rig.agmdocuments.com/AGM2018.html.

At the Meeting, shareholders of the Company will consider and vote upon proposals:

To ratify the appointment of Ernst & Young (Hellas) Certified Auditors Accountants S.A., as the Company's independent auditors for the fiscal year ending December 31, 2018 ("Proposal One");

To approve the special resolution required pursuant to the Companies Law (2016 Revision) of the laws of the Cayman Islands and the second amended and restated memorandum and articles of association of the Company to amend Article 32.4 of the second amended and restated memorandum and articles of association by deleting Article 32.4 of the second amended and restated memorandum and articles of association of the Company in its entirety and replacing it with the following (the "Constitutional Amendment"):

"The Directors, on behalf of the Company, shall purchase and maintain insurance for the benefit of any Director or other officer of the Company who is or was serving at the request of the Company as a director, officer, employee or agent of another corporation, partnership, joint venture, trust or other enterprise, including any Group Company against any expense, liability or loss asserted, against such person and incurred by such person in any such capacity, or arising out of such person's status as such, which, by virtue of any rule of law, would otherwise attach to such person in respect of any negligence, default, breach of duty or breach of trust of which such person may be guilty in relation to the Company, with coverage of not less than $400,000,000, or such lesser amount as may be approved by the Lender Directors."

("Proposal Two" and together with Proposal One, the "Proposals"); and

To transact such other business as may properly come before the Meeting or any adjournment thereof.

Adoption of Proposal One requires the affirmative vote of a majority of the votes cast at the Meeting by the holders of shares of stock entitled to vote thereon. Adoption of Proposal Two requires the affirmative vote of two-thirds of the shareholders as being entitled to do so, who vote in person or by proxy at the Meeting, either in person or by proxy (See bottom of page 6).

You are cordially invited to attend the Meeting in person. All shareholders must present a form of personal photo identification in order to be admitted to the Meeting. In addition, if your shares are held in the name of your broker, bank or other nominee and you wish to attend the Meeting, you must bring an account statement or letter from the broker, bank or other nominee indicating that you were the owner of the shares on January 31, 2018.

If you attend the Meeting, you may revoke your proxy and vote your shares in person. If your shares are held in the name of your broker, bank or other nominee and you intend to vote in person at the Meeting, you must present a legal proxy from your bank, broker or other nominee in order to vote. Shareholders should speak to their brokers, banks or other nominees in whose custody their shares are held for additional information.

WHETHER OR NOT YOU PLAN TO ATTEND THE MEETING, PLEASE COMPLETE, DATE, SIGN AND RETURN THE ENCLOSED PROXY IN THE ENCLOSED ENVELOPE, WHICH DOES NOT REQUIRE POSTAGE IF MAILED IN THE UNITED STATES. THE VOTE OF EVERY SHAREHOLDER IS IMPORTANT AND YOUR COOPERATION IN RETURNING YOUR EXECUTED PROXY PROMPTLY WILL BE APPRECIATED. ANY SIGNED PROXY RETURNED AND NOT COMPLETED WILL BE VOTED BY MANAGEMENT IN FAVOR OF ALL PROPOSALS PRESENTED IN THE PROXY STATEMENT.

The Company's 2016 Annual Report on Form 20-F (the "Annual Report"), which contains the Company's audited financial statements for the fiscal year ended December 31, 2016, along with the Company's Management's Discussion and Analysis of Financial Condition and Results of Operations and the unaudited interim condensed consolidated financial statements and related information and data as of and for the nine-month period ended September 30, 2017 filed on Form 6-K and other SEC filings are available on the Company's website at www.ocean-rig.com. Any shareholder may receive a hard copy of the Company's 2016 Annual Report, free of charge upon request.

Very truly yours,

George Economou
Chairman

OCEAN RIG UDW INC.
NOTICE OF ANNUAL GENERAL MEETING OF SHAREHOLDERS
TO BE HELD ON MARCH 5, 2018

NOTICE IS HEREBY given that the 2018 Annual General Meeting of Shareholders (the "Meeting") of Ocean Rig UDW Inc. (the "Company") will be held at 3rd Floor, Flagship Building, Harbour Drive, Grand Cayman, Cayman Islands on Monday, March 5, 2018 at 9:00am, local time, for the following purposes, of which items 1 and 2 are more completely set forth in the accompanying Proxy Statement:

To ratify the appointment of Ernst & Young (Hellas) Certified Auditors Accountants S.A., as the Company's independent auditors for the fiscal year ending December 31, 2018 ("Proposal One");

("Proposal Two" and together with Proposal One, the "Proposals"); and

To transact such other business as may properly come before the Meeting or any adjournment thereof.

The board of directors has fixed the close of business on January 31, 2018 as the record date (the "Record Date") for the determination of the shareholders entitled to receive notice and to vote at the Meeting or any adjournment thereof.

The Company's 2016 Annual Report on Form 20-F (the "2016 Annual Report"), which contains the Company's audited financial statements for the fiscal year ended December 31, 2016 along with the Company's Management's Discussion and Analysis of Financial Condition and Results of Operations and the unaudited interim condensed consolidated financial statements and related information and data as of and for the nine-month period ended September 30, 2017 filed on Form 6-K and other SEC filings are available on the Company's website at www.ocean-rig.com. Any shareholder may receive a hard copy of the Company's 2016 Annual Report, free of charge upon request. This Notice of the Meeting, the Proxy Statement and related materials, are available at http://ocean-rig.agmdocuments.com/AGM2018.html.

By Order of the Board of Directors

Iraklis Sbarounis
Secretary

February 14, 2018
Grand Cayman, Cayman Islands

PROXY STATEMENT
FOR
ANNUAL GENERAL MEETING OF SHAREHOLDERS
TO BE HELD ON MARCH 5, 2018

INFORMATION CONCERNING SOLICITATION AND VOTING

GENERAL

The enclosed proxy is solicited on behalf of the board of directors of Ocean Rig UDW Inc., a Cayman Islands exempted limited company (the "Company"), for use at the 2018 Annual General Meeting of Shareholders (the "Meeting") to be held on Monday, March 5, 2018 at 3rd Floor, Flagship Building, Harbour Drive, Grand Cayman, Cayman Islands at 9:00am, local time, and related materials, or at any adjournment or postponement thereof, for the purposes set forth herein and in the accompanying Notice of Annual General Meeting of Shareholders. This Proxy Statement and the accompanying form of proxy are expected to be sent to shareholders of the Company entitled to vote at the Meeting on or about February 14, 2018. These materials can also be found at http://ocean-rig.agmdocuments.com/AGM2018.html.

VOTING RIGHTS AND OUTSTANDING SHARES

On January 31, 2018 (the "Record Date"), the Company had issued 90,745,471 Class A common shares, par value $0.01 per share (the "Class A Common Shares") and 822,511 Class B Common Shares, par value $0.01 per share (the "Class B Common Shares" and together with the Class A Common Shares, the "Common Shares"), of which 91,567,982 Common Shares were considered issued and outstanding for voting purposes. Each shareholder of record at the close of business on the Record Date is entitled to one vote for each Common Share then held. One or more shareholders representing at least one-third of the Common Shares issued and outstanding and entitled to vote at the Meeting, whether represented in person or by proxy, shall be a quorum for the purposes of the Meeting. The Common Shares represented by any proxy in the enclosed form will be voted in accordance with the instructions given on the proxy if the proxy is properly executed and is received by the Company prior to the close of voting at the Meeting or any adjournment or postponement thereof. Any proxies returned without instructions will be voted FOR the proposals set forth on the Notice of Annual General Meeting of Shareholders.

In the event that a quorum is not present at the Meeting within half an hour from the time appointed for a meeting to commence or, even if a quorum is so present, in the event that sufficient votes in favor of the positions recommended by the board of directors on the proposals described in this Proxy Statement are not timely received, the chairman of the meeting shall have the power to adjourn the Meeting until a quorum shall be present or sufficient votes in favor of the positions recommended by the board of directors are received. If the Meeting is adjourned for reasons other than a lack of quorum, no further notice of the adjourned Meeting will be required other than announcement at the Meeting of the time and place to which the Meeting is adjourned in order to permit further solicitation of proxies.

The Class A Common Shares are listed on The NASDAQ Global Select Market under the symbol "ORIG". The Class B Common Shares are not publicly traded.

REVOCABILITY OF PROXIES

A shareholder giving a proxy may revoke it at any time before it is exercised. A proxy may be revoked by filing with the Secretary of the Company at the Company's principal executive office, c/o Ocean Rig Cayman Management Services SEZC Limited, 3rd Floor, Flagship Building, Harbour Drive, Grand Cayman, Cayman Islands¹, a written notice of revocation by a duly executed proxy bearing a later date, or by attending the Meeting and voting in person. If your shares are held in the name of your broker, bank or other nominee and you intend to vote in person at the Meeting, you must present a legal proxy from your bank, broker or other nominee in order to vote. Shareholders should speak to their brokers, banks or other nominees in whose custody their shares are held for additional information.

¹ Note: this address is for courier delivery only and will not receive mail by post.

PROPOSAL ONE

RATIFICATION OF THE APPOINTMENT OF
INDEPENDENT AUDITORS

The board of directors is submitting for ratification at the Meeting the appointment of Ernst & Young (Hellas) Certified Auditors Accountants S.A. ("Ernst & Young"), as the Company's independent auditors for the fiscal year ending December 31, 2018.

Ernst & Young has advised the Company that the firm does not have any direct or indirect financial interest in the Company, nor has such firm had any such interest in connection with the Company during the past three fiscal years other than in its capacity as the Company's independent auditors.

All services rendered by the independent auditors are subject to review by the audit committee of the Company's board of directors.

Required Vote. Approval of Proposal One will require the affirmative vote of a majority of the votes cast at the Meeting by the holders of Common Shares entitled to vote thereon.

THE BOARD OF DIRECTORS UNANIMOUSLY RECOMMENDS A VOTE FOR RATIFICATION OF THE APPOINTMENT OF ERNST & YOUNG AS INDEPENDENT AUDITORS OF THE COMPANY FOR THE FISCAL YEAR ENDING DECEMBER 31, 2018. UNLESS REVOKED AS PROVIDED ABOVE, PROXIES RECEIVED BY MANAGEMENT WILL BE VOTED IN FAVOR OF SUCH APPROVAL UNLESS A CONTRARY VOTE IS SPECIFIED.

PROPOSAL TWO

AMENDMENT TO ARTICLE 32.4 OF THE SECOND AMENDED AND RESTATED ARTICLES OF ASSOCIATION OF THE COMPANY

The Company is submitting for approval at the Meeting a proposal for a special resolution pursuant to the companies law (2016 revision) of the laws of the cayman islands and the second amended and restated memorandum and articles of association of the company to amend article 32.4 of the second amended and restated memorandum and articles of association by deleting article 32.4 of the second amended and restated memorandum and articles of association of the company in its entirety and replacing it with the following:

The directors have recommended that Article 32.4 be amended to allow the amount of directors and officers insurance coverage of not less than $400,000,000, or such lesser amount as may be approved by the Lender Directors (as defined in the Second Amended and Restated Memorandum and Articles of Association) in order to allow the Company flexibility to obtain the most attractive terms.

Required Vote. Approval of Proposal Two will require the affirmative vote of two-thirds of the shareholders as being entitled to do so, who vote in person or by proxy at the Meeting, either in person or by proxy.

THE BOARD OF DIRECTORS UNANIMOUSLY RECOMMENDS A VOTE TO AMEND ARTICLE 32.4 OF THE SECOND AMENDED AND RESTATED ARTICLES OF ASSOCIATION OF THE COMPANY AS DETAILED ABOVE. UNLESS REVOKED AS PROVIDED ABOVE, PROXIES RECEIVED BY MANAGEMENT WILL BE VOTED IN FAVOR OF SUCH APPROVAL UNLESS A CONTRARY VOTE IS SPECIFIED.

SOLICITATION

The cost of preparing and soliciting proxies will be borne by the Company. Solicitation will be made primarily by mail, but shareholders may be solicited by telephone, e-mail, or personal contact.

EFFECT OF ABSTENTIONS

Abstentions will not be counted in determining whether Proposals One or Two have been adopted.

OTHER MATTERS

No other matters are expected to be presented for action at the Meeting. Should any additional matter come before the Meeting, it is intended that proxies in the accompanying form will be voted in accordance with the judgment of the person or persons named in the proxy.

By Order of the Board of Directors

Iraklis Sbarounis
Secretary

February 14, 2018
Grand Cayman, Cayman Islands

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