Supplemental Prospectus (Form 424B3)

Filed Pursuant to Rule 424(b)(3)

Registration No. 333-284263

PROSPECTUS SUPPLEMENT

To Prospectus dated February 7, 2025

Up to 73,333 Shares of Common Stock

Up to 31,145,319 Shares of Common Stock Issuable Upon Conversion of Notes

Up to 600,000 Shares of Common Stock Issuable Upon Exercise of Warrants

Adagio Medical Holdings, Inc.

This prospectus supplement updates and supplements the information contained in the prospectus dated February 7, 2025 (as may be supplemented or amended from time to time, the "Prospectus"), which forms part of our registration statement on Form S-1 (File No. 333-284263) with the information contained in our Current Report on Form 8-K that was filed with the Securities and Exchange Commission on October 10, 2025 (the "Current Report"). Accordingly, we have attached the Current Report to this prospectus supplement.

The Prospectus and this prospectus supplement relate to the offer, sale or other disposition from time to time of up to 31,818,652 shares of our common stock, $0.0001 par value per share (the "Common Stock"), by the selling stockholders named in this prospectus or their permitted transferees (the "selling stockholders"), consisting of (i) 73,333 shares of Common Stock (the "Registration Delay Shares") issued pursuant to the terms of the Convert Waivers (as defined below), (ii) up to 31,145,319 shares of Common Stock (excluding the shares of Common Stock underlying the Warrants (as defined below)) (the "Convertible Note Shares") issuable upon the conversion of those certain 13% senior secured convertible notes, with a conversion price of $10.00 per share, subject to adjustment (the "Convertible Notes") issuable pursuant to that certain securities purchase agreement, dated February 13, 2024, by and among us and those certain investors (the "Convert Investors"), and any assignment thereunder (the "Convertible Security Subscription Agreement"), and that certain note purchase agreement, dated February 13, 2024, by and among us, Adagio Medical, Inc., a Delaware corporation, and that certain investor party thereto, and (iii) up to 600,000 shares of Common Stock (the "Warrant Shares") issuable upon exercise of those warrants to purchase shares of Common Stock, with an exercise price of $24.00 per share (the "Warrants"), issued pursuant to the Convertible Security Subscription Agreement.

You should read this prospectus supplement in conjunction with the Prospectus. This prospectus supplement is qualified by reference to the Prospectus except to the extent that the information in this prospectus supplement supersedes the information contained in the Prospectus. This prospectus supplement is not complete without, and may not be delivered or utilized except in connection with, the Prospectus. If there is any inconsistency between the information in the Prospectus and this prospectus supplement, you should rely on the information in this prospectus supplement. Terms used in this prospectus supplement but not defined herein shall have the meanings given to such terms in the Prospectus.

Our Common Stock is listed on The Nasdaq Capital Market under the symbol "ADGM". On October 9, 2025, the last reported sales price of our Common Stock was $2.32 per share.

We are an "emerging growth company" as defined under U.S. federal securities laws and, as such, have elected to comply with reduced public company reporting requirements. This prospectus complies with the requirements that apply to an issuer that is an emerging growth company.

Investing in our securities involves a high degree of risk. You should review carefully the risks and uncertainties described in the section titled "Risk Factors" beginning on page 10 of the prospectus, and under similar headings in any amendments or supplements to the prospectus.

Neither the Securities and Exchange Commission nor any state securities commission has approved or disapproved of these securities, or passed upon the accuracy or adequacy of the prospectus. Any representation to the contrary is a criminal offense.

The date of this prospectus supplement is October 10, 2025.