| Cover | Aug. 19, 2024 |
| Cover [Abstract] | |
| Document Type | 8-K |
| Amendment Flag | false |
| Document Period End Date | Aug. 19, 2024 |
| Entity File Number | 001-42199 |
| Entity Registrant Name | ADAGIO MEDICAL HOLDINGS, INC. |
| Entity Central Index Key | 0002006986 |
| Entity Tax Identification Number | 99-1151466 |
| Entity Incorporation, State or Country Code | DE |
| Entity Address, Address Line One | 26051 Merit Circle |
| Entity Address, Address Line Two | Suite 102 |
| Entity Address, City or Town | Laguna Hills |
| Entity Address, State or Province | CA |
| Entity Address, Postal Zip Code | 92653 |
| City Area Code | 949 |
| Local Phone Number | 348-1188 |
| Written Communications | false |
| Soliciting Material | false |
| Pre-commencement Tender Offer | false |
| Pre-commencement Issuer Tender Offer | false |
| Title of 12(b) Security | Common Stock, par value $0.0001 per share |
| Trading Symbol | ADGM |
| Security Exchange Name | NASDAQ |
| Entity Emerging Growth Company | true |
| Elected Not To Use the Extended Transition Period | false |
