Lord Chief Justice Lord Burnett and Lord Justice Holroyde ruled in favour of the US on Friday.
Judge Holroyde said he was satisfied with a package of assurances given by the US about the conditions of Mr Assange’s detention including a pledge not to hold him in a so-called “ADX” maximum-security prison in Colorado and that he would be transferred to Australia to serve his sentence if convicted.
“That conclusion is sufficient to determine this appeal in the USA’s favour,” the judges said.
The case will now go back to the lower court to be considered again, and will likely end up in the Supreme Court, the final court of appeal.
Mr Assange, who denies any wrongdoing, was not in court. He remains in London’s high-security Belmarsh prison, where he has been for more than two and a half years.
His partner, Stella Moris, said his legal team would appeal the decision.
“How can it be fair, how can it be right, how can it be possible, to extradite Julian to the very country which plotted to kill him?” she said. “We will appeal this decision at the earliest possible moment.”
The long-running case has become a cause celebre for free speech, with Mr Assange’s supporters arguing WikiLeaks has the same rights as other media to publish secret material in the public interest.
Pro-Assange supporters gathered outside the court, waving placards and demanding his immediate release from a high-security jail in southeast London.
The US government has indicated Mr Assange on 18 charges relating to WikiLeaks’ release of 500,000 secret files on the conflicts in Afghanistan and Iraq.
If extradited, tried and convicted, he could be jailed for up to 175 years, although the exact sentence is difficult to estimate and could be shorter.
Mr Assange has been in custody since 2019, despite having served a previous sentence for breaching bail conditions in a separate case.
The maverick publisher spent seven years at Ecuador’s embassy in London to avoid being removed to Sweden to face sexual assault allegations that were later dropped.
While at the South American country’s mission, he fathered two children with Ms Moris, who is a member of his legal team.
British prison authorities last month gave the couple permission to marry at the Belmarsh high-security prison in southeast London.
With additional reporting by Reuters and SBS News.