Exhibit 5.1

Transocean Ltd. Turmstrasse 30 6312 Steinhausen Switzerland	Homburger AG Prime Tower Hardstrasse 201 / CH-8005 Zurich P.O. Box 314 / CH-8037 T +41 43 222 10 00 F +41 43 222 15 00 lawyers@homburger.ch
June 16, 2023
Transocean Ltd.

Ladies and Gentlemen:

We have acted as special Swiss counsel to Transocean Ltd., a company limited by shares incorporated under the laws of Switzerland (the Company), in connection with the Registration Statement on Form S-8 (the Registration Statement) to be filed with the United States Securities and Exchange Commission (the SEC) on the date hereof under the Securities Act of 1933, as amended (the Act), with respect to the registration of 30,000,000 registered shares of the Company, each with a nominal value of CHF 0.10 (the registered shares of the Company hereinafter generally referred to as the Shares) in connection with and following the amendment and restatement of the Company's 2015 Long-Term Incentive Plan, as amended and restated effective May 11, 2023 (the Plan). As such counsel, we have been requested to give our opinion as to certain legal matters under Swiss law.

Capitalized terms used herein shall have the meaning attributed to them in the Documents (as defined below) unless otherwise defined herein.

I. Basis of Opinion

This opinion is confined to and given on the basis of the laws of Switzerland in force at the date hereof as currently applied by the Swiss courts. In the absence of explicit statutory law, we base our opinion solely on our independent professional judgment. This opinion is also confined to the matters stated herein and is not to be read as extending, by implication or otherwise, to any document referred to in the Documents (other than listed below) or any other matter.

For purposes of this opinion, we have not conducted any due diligence or similar investigation as to factual circumstances, which are or may be referred to in the Documents, and we express no opinion as to the accuracy of representations and warranties of facts set out in the Documents or the factual background assumed therein.

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For the purpose of giving this opinion, we have only examined originals or copies of the following documents (collectively the Documents):

(i)A copy of the resolution passed by the shareholders of the Company at the Company's annual general meeting (the AGM) held on May 11, 2023 (the Shareholder Resolution), as reflected in the minutes of such meeting, dated May 11, 2023, regarding the approval by the Company's shareholders of, among other things, the amendment and restatement of the Plan and the capital authorization for share-based incentive plans through the creation of a capital band;

(ii)A copy of the resolutions of the Company's board of directors (the Board) by written consent as of March 10, 2023 (the Board Resolutions), including, among other things, a resolution approving the amendment and the restatement of the Plan, which increased the number of Shares available for issuance thereunder by 30,000,000 Shares, and a resolution recommending that the Company's shareholders approve at the Company's 2023 annual general meeting of shareholders the authorization of the issuance of Shares using a capital band (the Capital Band) that may be used, among other purposes, to satisfy the Company's equity incentive plans obligations pursuant to the Plan;

(iii)A copy of the Plan;

(iv)A copy of the Articles of Association (Statuten) of the Company in the form deposited with the Commercial Register of the Canton of Zug, Switzerland, dated May 11, 2023 (the Articles of Association), including the Capital Band pursuant to Article 5 of the Articles of Association and the conditional share capital pursuant to Article 6 of the Articles of Association (such conditional share capital hereinafter the Conditional Share Capital);

(v)A copy of the Organizational Regulations (Organisationsreglement) of the Company, dated as of May 12, 2023 (the Organizational Regulations); and

(vi)A copy of an online excerpt from the Commercial Register of the Canton of Zug, Switzerland, for the Company, dated as of June 15, 2023 (the Excerpt).

No documents, other than the Documents, have been reviewed by us in connection with this opinion. Accordingly, we shall limit our opinion to the Documents and their legal implications under Swiss law.

In this opinion, Swiss legal concepts are expressed in English terms and not in their original language. These concepts may not be identical to the concepts described by the same English terms as they exist under the laws of other jurisdictions.

II. Assumptions

In rendering the opinion below, we have assumed the following:

(a) The filing of the Registration Statement with the SEC has been authorized by all necessary actions under all applicable laws other than Swiss law;

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(b) all documents produced to us as originals and the originals of all documents produced to us as copies were duly executed and certified, as applicable, by the individuals purported to have executed or certified, as the case may be, such documents, and any electronic or facsimile signatures thereon have been produced and used in accordance with applicable internal rules and/or procedures and the individual to whom any such electronic or facsimile signature belongs has consented to the use of his or her signature for each such document on which it appears;

(c) all factual information contained in, or material statements given in connection with, the Documents are true and accurate;

(d) the Documents are within the capacity and power of, and have been validly authorized and executed by the Company;

(e) the Registration Statement has been filed by the Company;

(f) any Shares issued for use under the Plan will be listed on the New York Stock Exchange in accordance with applicable laws and regulations;

(g) all authorizations, approvals, consents, licenses, exemptions and other requirements for the filing of the Registration Statement or for any other activities carried on in view of, or in connection with, the performance of the obligations expressed to be undertaken by the Company in the Registration Statement have been duly obtained and are and will remain in full force and effect, and any related conditions to which the parties thereto are subject have been satisfied;

(h) the exercise notice with respect to Shares issued out of the Conditional Share Capital will be duly delivered in accordance with Swiss law and the Plan;

(i) to the extent the Company issues Shares based on Conditional Share Capital, the performance of the contribution in money shall be made at a banking institution subject to the Federal Law of November 8, 1934, Relating to Banks and Savings Banks, as amended;

(j) any Shares issued based on the Conditional Capital will be recorded in the Company's uncertificated securities register (Wertrechtebuch);

(k) to the extent the Company issues Shares based on the Capital Band, the number of Shares issued based on the Capital Band will not exceed the maximum number of Shares issuable pursuant to Article 5 para 5 of the Articles of Association;  

(l) (x) the Excerpt is correct, complete and up-to-date as of the date hereof and (y) the Articles of Association, the Organizational Regulations and the other Documents are in full force and effect and have not been amended subsequent to the respective dates set forth above; and

(m) each of the Shareholder Resolution and the Board Resolutions, (i) has been duly resolved in a meeting duly convened and otherwise in the manner set forth therein, and (ii) has not been rescinded or amended and is in full force and effect.

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III. Opinion

Based on the foregoing and subject to the qualifications set out below, we are of the opinion that as of the date hereof:

1. The Company is a corporation (Aktiengesellschaft) duly incorporated and validly existing under the laws of Switzerland with all requisite corporate power and authority to enter into, to perform and to conduct its business as described in the Articles of Association.

2. The Company's share capital registered in the Commercial Register of the Canton of Zug amounts to CHF 83,184,490, divided into 831,844,900 Shares. Such Shares have been validly issued, fully paid and are non-assessable.

3. The Shares that may be issued based on the Conditional Share Capital, if and when such Shares are issued pursuant to the Plan, and after the subscription price for such Shares has been paid-in in accordance with the Articles of Association (as amended from time to time) and Swiss law, will be validly issued, fully paid and non-assessable.

4. The Shares that may be issued based on the Capital Band, if and when issued by the Company in accordance with Swiss law, the Articles of Association (as amended from time to time) and the Organizational Regulations (as amended from time to time) and (iii) registered in the competent commercial register in Switzerland and the Company's uncertificated securities register (Wertrechtebuch), will be validly issued, fully paid and non-assessable.

IV. Qualifications

The above opinions are subject to the following qualifications:

(a) The lawyers of our firm are members of the Zurich bar and do not hold themselves out to be experts in any laws other than the laws of Switzerland. Accordingly, we are opining herein as to Swiss law only and we express no opinion with respect to the applicability thereto, or the effect thereon, of the laws of any other jurisdiction.

(b) We note that under Swiss law, Shares issued based on Conditional Capital cannot be paid in by way of a contribution in kind.

(c) The exercise of voting rights and rights related thereto with respect to any Shares is only permissible after registration in the Company's share register as a shareholder with voting rights in accordance with the provisions of, and subject to the limitations provided in, the Articles of Association.

(d) We express no opinion as to any commercial, accounting, tax, calculating, auditing or other non-legal matter.

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(e) We have not investigated or verified the truth or accuracy of the information contained in the Registration Statement, nor have we been responsible for ensuring that no material information has been omitted from it;

(f) Any issuance of the Shares based on Conditional Share Capital must be confirmed by the auditor of the Company, and amended Articles of Association of the Company reflecting the issuance of Shares from Conditional Share Capital, together with said confirmation by the Company's auditor, must be filed with the competent commercial register no later than three months after the end of the Company's fiscal year; and

(g) The Capital Band and the authority to issue any Shares based thereon expires on May 11, 2028.

We have issued this opinion as of the date hereof and we assume no obligation to advise you of any changes that are made or brought to our attention hereafter.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act.

This opinion is governed by and shall be construed in accordance with the laws of Switzerland.

Sincerely yours
HOMBURGER AG

/s/ David Oser​ ​​ ​David Oser

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