The decision now rests with interior minister Priti Patel, although Assange's lawyers may still appeal to the High Court if she approves the extradition.
Assange, 50, and his South Africa-born partner Stella Moris, 38, have two sons together- four-year-old Gabriel and two-year-old Max.
The ruling brings the long-running legal saga in the UK courts closer to a conclusion unless Assange's lawyers launch a challenge on a separate point in the case.
The High Court in London allowed Assange to appeal its decision that he could be sent to the U.S to stand trial on espionage charges.
The decision is the latest step in Assange’s long battle to avoid being sent to the United States to face espionage charges over WikiLeaks’ publication of classified documents more than a decade ago.
Julian Assange had been on anti-stroke medication and had an MRI scan while held in the prison as his health had been on the decline.
The HC ruling oververturned a lower court decision that the embattled WikiLeaks founder could not be sent to America to face spying charges due to concerns over his mental health.
US authorities have also told British judges that if they agree to extradite Julian Assange, he could serve any US prison sentence he receives in his native Australia.
The couple began their relationship during Assange's seven years living in the Ecuadorian Embassy in London to avoid extradition to Sweden on unrelated sex offenses allegations.
WikiLeaks founder Julian Assange is currently being held at London’s high-security Belmarsh Prison.
In January, a lower court judge refused an American request to extradite Assange on spying charges over WikiLeaks' publication of secret military documents a decade ago.
"New Trump book 'Fire and Fury' by Michael Wolff. Full PDF," WikiLeaks posted on Twitter on Sunday, along with a link to a Google Drive containing the full text of the book.
The statement by the Unique Identification Authority of India came after WikiLeaks hinted that CIA had allegedly accessed the Aadhaar database.
Cross Match technologies also provides biometric solutions to the Unique Identification Authority of India, the statutory body for Aadhaar.
Swedish prosecutors on Friday dropped their investigation, but Assange still faces the risk of arrest in Britain.