Musician and songwriter Roger Waters (L) and actress Susan Sarandon (R) speak during a protest against a high court ruling allowing the extradition to the US of WikiLeaks founder Julian Assange, outside the British consulate in New York on December 13, 2021. AFP
The December 10 decision by the High Court in London reversed an earlier judgement by a British magistrates' court that it would be "oppressive" to extradite the 50-year-old Australian to the US justice system due to his mental health and the risk of suicide.
The United States wants Assange to face trial for WikiLeaks' publication in 2010 of classified military documents relating to its wars in Afghanistan and Iraq.
The US government has indicted Assange on 18 charges relating to the release of 500,000 secret files on the conflicts.
He could be jailed for up to 175 years in the US, although the exact sentence is difficult to estimate.
Assange's fiancee Stella Moris, herself a lawyer, said on Twitter that his lawyers filed an appeal to the extradition ruling on Thursday.
Moris, who has two children with Assange, said no decision regarding a Supreme Court appeal can be expected before the third week of January.
A two-day hearing in October saw lawyers for the United States argue that a lower court judge had not given sufficient weight to other expert testimony about his mental state.
They also pointed to diplomatic assurances provided since the January decision that Assange would not be held in punishing isolation at a federal supermax prison, and would receive appropriate care.
Approving the appeal, two judges at the High Court in London accepted the new assurances, noting they were not unusual in such cases and "solemn undertakings offered by one government to another".
Assange has been in custody since 2019, despite having served a previous sentence for breaching bail conditions in a separate case.
He spent seven years at Ecuador's embassy in London to avoid being removed to Sweden to face sexual assault allegations that were later dropped.