However, his wife, Stella, said he would launch a fresh appeal on Tuesday (13 June).
The rejection of his appeal occurred on 6 June and the decision was made by a single judge, according to the organisation Reporters Without Borders.
The initial appeal came after then British home secretary Priti Patel approved the extradition of Assange to stand trial in the US.
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On 14 March, the UK Supreme Court had rejected an appeal from Assange to hear arguments against his extradition.
In January, the High Court refused a request from Assange's lawyers to appeal directly to the Supreme Court, leaving it to the higher court to decide on whether it would hear a challenge.
On 10 December 2021, a two-bench High Court panel reversed a 4 January lower court verdict the same year to deny the US the right to extradite Assange to try him on criminal charges in Washington.
British District Judge Vanessa Baraister had ruled in January 2021 that Assange should not be extradited, saying the risk he would commit suicide in a US jail was too high.
In a tweet, Stella Assange said: "On Tuesday next week, my husband Julian Assange will make a renewed application for appeal to the High Court.
"The matter will then proceed to a public hearing before two new judges at the High Court and we remain optimistic that we will prevail and that Julian will not be extradited to the United States where he faces charges that could result in him spending the rest of his life in a maximum security prison for publishing true information that revealed war crimes committed by the US Government."
Assange, an Australian citizen, was arrested in 2019 and jailed at the maximum security prison in Belmarsh after he had been given refuge in the Ecuadorian embassy in London for seven years. He has remained at the prison while his appeals are decided.
Reporters Without Borders director of campaigns Rebecca Vincent said in a statement: “It is absurd that a single judge can issue a three-page decision that could land Julian Assange in prison for the rest of his life and permanently impact the climate for journalism around the world.
"The historical weight of what happens next cannot be overstated; it is time to put a stop to this relentless targeting of Assange and act instead to protect journalism and press freedom.
"Our call on [US] President [Joe] Biden is now more urgent than ever: drop these charges, close the case against Assange, and allow for his release without further delay."