Exhibit 5.1



910 Louisiana Houston, Texas 77002-4995 TEL +1 713.229.1234 FAX +1 713.229.1522 BakerBotts.com	AUSTIN Brussels DALLAS DUBAI HOUSTON LONDON	NEW YORK PALO ALTO Riyadh San Francisco SINGAPORE WASHINGTON

June 28, 2024

Transocean Ltd.

Transocean Inc.

c/o Transocean Offshore Deepwater Drilling Inc.

1414 Enclave Parkway

Houston, Texas 77077

Ladies and Gentlemen:

As set forth in the Registration Statement on Form S-3 (the “Registration Statement”) to be filed on the date hereof by Transocean Ltd., a corporation incorporated under the laws of Switzerland (“Transocean”), and Transocean Inc., an exempted company incorporated under the laws of the Cayman Islands and a wholly owned subsidiary of Transocean (“TINC” and, together with Transocean, the “Transocean Parties”), with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), relating to the offering of securities that may be issued and sold by the Transocean Parties from time to time pursuant to Rule 415 under the Act, certain legal matters in connection with such securities are being passed upon for you by us. Such securities consist of (i) shares of Transocean, par value USD 0.10 per share (the “Shares”), (ii) senior debt securities of TINC (the “Senior Debt Securities”) and subordinated debt securities of TINC (the “Subordinated Debt Securities” and together with the Senior Debt Securities, the “Debt Securities”), (iii) warrants to purchase Shares or Debt Securities or other securities or any combination of the foregoing (“Warrants”), (iv) purchase contracts with regard to Shares, Debt Securities or securities of third parties, including any of Transocean’s affiliates, a basket of such securities, an index or indices of such securities or any combination of the foregoing (“Purchase Contracts”), (v) rights for the purchase of Shares or Debt Securities (“Rights”), (vi) units consisting of any combination of Shares, Debt Securities, Warrants, Purchase Contracts or Rights (“Units”) and (vii) Transocean’s guarantee of the Debt Securities (“Guarantee”, and with the Shares, Debt Securities, Warrants, Purchase Contracts, Rights and Units, the “Securities”). At your request, this opinion is being furnished to you for filing as Exhibit 5.1 to the Registration Statement.

The Senior Debt Securities and any related Guarantee of such Senior Debt Securities by Transocean are to be issued pursuant to the indenture dated as of December 11, 2007 (the “Base Senior Indenture”), between TINC, as issuer, and Wells Fargo Bank, National

Association, as supplemented by the Third Supplemental Indenture, dated as of December 18, 2008 (the “Supplemental Senior Indenture” and, together with the Base Senior Indenture, the “Senior Indenture”), among Transocean, TINC, and Wells Fargo Bank, National Association (the “Trustee”), as trustee. The Subordinated Debt Securities and any related Guarantee of such Subordinated Debt Securities by Transocean are to be issued pursuant to a subordinated indenture in the form filed as Exhibit 4.3 to the Registration Statement (the “Base Subordinated Indenture”), as supplemented by the form of first supplemental indenture to the Base Subordinated Indenture in the form filed as Exhibit 4.4 to the Registration Statement (the “Supplemental Subordinated Indenture” and, together with the Based Subordinated Indenture, the “Subordinated Indenture,” and the Subordinated Indenture together with Senior Indenture, the “Indentures”). The Indentures each will be supplemented, in connection with the issuance of each series of Debt Securities, as the case may be, by a supplemental indenture, officers’ certificate or other writing thereunder establishing the form and terms of such series.

In our capacity as your counsel in the connection referred to above, we have examined originals, or copies certified or otherwise identified, of:

(i)

the articles of association and organizational regulations of Transocean (collectively, the “Transocean Charter Documents”);

(ii)

the amended and restated memorandum and articles of association of TINC (the “TINC Charter Documents”);

(iii)

the Indentures;

(iv)

corporate records of the Transocean Parties, certificates of public officials and of representatives of the Transocean Parties, statutes and other instruments and documents as a basis for the opinions hereinafter expressed.

In giving such opinions, we have relied, to the extent we deem appropriate without independent investigation or verification, upon certificates of officers of the Transocean Parties and of public officials with respect to the accuracy of the material factual matters contained in such certificates. In giving the opinions below, we have assumed that the signatures on all documents examined by us are genuine, that all documents submitted to us as originals are accurate and complete, that all documents submitted to us as copies are true, correct and complete copies of the originals thereof and that all information submitted to us is accurate and complete. Further, we have assumed that:

(a) the Registration Statement and any amendments thereto (including post-effective amendments) will have become effective under the Act;

(b) a prospectus supplement will have been prepared and filed with the Commission describing the Securities offered thereby;

(c) all Securities will be offered, issued and sold in compliance with applicable federal and state securities laws and in the manner stated in the Registration Statement and the applicable prospectus supplement;

(d) in the case of any Securities issued by Transocean, the board of directors of Transocean or, to the extent permitted by the laws of Switzerland and the Transocean Charter Documents, a duly constituted and acting committee thereof (such board or committee thereof being hereinafter referred to as the “Board”), will have taken all necessary corporate action to authorize the issuance of such Securities and any other securities issuable on the conversion, exchange, redemption or exercise thereof, and to authorize the terms of the offering and sale of such Securities and related matters;

(e) in the case of any Securities issued by TINC, the board of directors of TINC or, to the extent permitted by the laws of the Cayman Islands and the TINC Charter Documents, a duly constituted and acting committee thereof (such board or committee thereof being hereinafter referred to as the “TINC Board”), will have taken all necessary corporate action to authorize the issuance of the Securities, and to authorize the terms of the offering and sale of such Securities and related matters;

(f) a definitive purchase, underwriting or similar agreement with respect to any Securities offered will have been duly authorized and validly executed and delivered by Transocean or TINC, as applicable, and the other parties thereto (the “Purchase Agreement”);

(g) any securities issuable upon conversion, exchange, redemption or exercise of any Securities being offered will have been duly authorized, created and, if appropriate, reserved for issuance upon such conversion, exchange, redemption or exercise;

(h) all Securities will be delivered (i) in accordance with the provisions of the applicable Purchase Agreement approved by the Board or the TINC Board, as applicable, upon receipt of the consideration therein provided or (ii) upon conversion, exchange, redemption or exercise of any other security, in accordance with the terms of such security or the instrument governing such security providing for such conversion, exchange, redemption or exercise as approved by the Board or the TINC Board, as applicable, for the consideration approved by the Board or the TINC Board, as applicable;

(i) in the case of any series of Securities issuable under an Indenture: (i) the Board and the TINC Board, as applicable, will have taken all necessary corporate action to designate and establish the terms of such Debt Securities and related Guarantees in accordance with the terms of the applicable Indenture, and such Debt Securities will not include any provision that is unenforceable, (ii) the applicable Indenture will have become qualified under the Trust Indenture Act of 1939, as amended, and (iii) forms of Debt Securities and Guarantees complying with the terms of the applicable Indenture and evidencing such Debt Securities and Guarantees will have been duly executed, authenticated, issued and delivered in accordance with the provisions of such Indenture;

(j) in the case of Warrants, (i) the Board or the TINC Board, as applicable, will have taken all necessary corporate action to authorize the terms of such Warrants and the warrant

agreement relating thereto, (ii) such warrant agreement will have been duly executed and delivered by Transocean or TINC, as applicable, and the warrant agent thereunder appointed by Transocean or TINC, as applicable, (iii) neither such Warrants nor such warrant agreement will include any provision that is unenforceable and (iv) such Warrants or certificates representing such Warrants will be duly executed, countersigned, registered and delivered in accordance with the provisions of such warrant agreement and the applicable Purchase Agreement to the purchasers thereof upon payment of the agreed-upon consideration therefor;

(k) in the case of the Purchase Contracts, (i) the Board or the TINC Board, as applicable, will have taken all necessary corporate action to establish the terms thereof and approve the purchase contract agreement relating thereto, (ii) such Purchase Contracts will have been duly executed and delivered by Transocean or TINC, as applicable, and the other parties thereto and (iii) such Purchase Contracts will not include any provision that is unenforceable;

(l) in the case of Rights, (i) the Board or the TINC Board, as applicable, will have taken all necessary corporate action to authorize the terms of such Rights, (ii) the applicable rights agreement will be duly authorized by Transocean or TINC, as applicable, and duly executed and delivered by Transocean or TINC, as applicable, and the rights agent thereunder appointed by the Transocean or TINC, as applicable, and (iii) such Rights or certificates representing such Rights, if any, will have been duly executed, countersigned, registered and delivered in accordance with the provisions of such rights agreement and the applicable Purchase Agreement; and

(m) in the case of Units, (i) the Board or the TINC Board, as applicable, will have taken all necessary corporate action to establish the terms of such Units and the terms of the Securities such Units include, (ii) the terms of the Units and the related Securities and their issuance and sale will have been duly established in conformity with the applicable contracts, agreements or indentures that are a component of the offered Units (including authorization of the issuance of any Securities to be issued pursuant to such Units) and (iii) any agreement or other instrument establishing such Unit or defining the rights of holders of such Unit will not contain any provision that is unenforceable.

On the basis of the foregoing, and subject to the assumptions, limitations and qualifications hereinafter set forth, we are of the opinion that:

1. The Debt Securities will, when issued, constitute legal, valid and binding obligations of TINC, enforceable against TINC in accordance with their terms, except as that enforcement is subject to (a) any applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent transfer or conveyance or other laws relating to or affecting creditors’ rights generally, (b) general principles of equity (regardless of whether that enforceability is considered in a proceeding in equity or at law) and (c) any implied covenants of good faith and fair dealing. The Debt Securities covered by the opinion in this paragraph include any Debt Securities that may be issued under the terms or as part of Warrants, Purchase Contracts, Rights or Units.

2. The Guarantees will, when issued, constitute legal, valid and binding obligations of Transocean, enforceable against Transocean in accordance with their terms, except as that enforcement is subject to (a) any applicable bankruptcy, insolvency, reorganization,

moratorium, fraudulent transfer or conveyance or other laws relating to or affecting creditors’ rights generally, (b) general principles of equity (regardless of whether that enforceability is considered in a proceeding in equity or at law) and (c) any implied covenants of good faith and fair dealing. The Guarantees covered by the opinion in this paragraph include any Guarantees that may be issued under the terms or as part of Warrants, Purchase Contracts, Rights or Units.

The opinions set forth above in this letter are limited in all respects to matters of applicable federal law of the United States of America and the laws of the State of New York.

With respect to matters governed by the laws of Switzerland, we have relied, with the consent of such counsel, on the opinion, filed as Exhibit 5.2 to the Registration Statement, of Homburger AG. With respect to matters governed by the laws of the Cayman Islands, we have relied, with the consent of such counsel, on the opinion, filed as Exhibit 5.3 to the Registration Statement, of Carey Olsen Cayman Limited. Our opinions with respect to such matters are subject to the same qualifications, assumptions and limitations as are set forth in such opinions.

We hereby consent to the filing of this opinion of counsel as Exhibit 5.1 to the Registration Statement. We also consent to the references to our Firm under the heading “Legal Matters” in the prospectuses forming a part of the Registration Statement. In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ Baker Botts L.L.P.