A statement from WikiLeaks said the hearing would be held before two judges who would review an earlier High Court decision on 6 June 2023 which refused Assange permission to appeal against his extradition.
A second appeal was filed on 13 June. Assange's extradition was given the green light in June 2022 by then British Home Secretary Priti Patel.
Assange has been held in the high-security Belmarsh Prison since he was arrested following an US extradition request on 11 April 2019.
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Apart from his supporters, Assange has received backing from both American and Australian politicians. In November, 16 American politicians from both sides of the political spectrum wrote to US President Joe Biden asking him to end the extradition bid.
In September, 63 members of Australia's Parliament published a letter in the Washington Post, calling for Assange to be freed. Six of this group travelled to Washington DC to lobby for the charges against Assange to be dropped.
John Rees of the Free Assange campaign, said: "The US is attempting to convict Assange under the 1917 Espionage Act. If they get away with it, they will have succeeded in redefining journalism as spying.
"Every journalist will be intimidated. Every newspaper and broadcaster will look at material critical of the government and feel significant pressure not to publish for fear of prosecution and imprisonment.
"This is the most important press freedom case of the 21st century and we need to ensure we don't lost any hard-won freedoms."
WikiLeaks editor-in-chief Kristinn Hrafnsson said: "There is no press without the protection to operate freely. Julian's case is a landmark moment; the UK needs to decide if it wishes to be a haven for free press or if it wishes to be complicit in the degradation of a core value of our democracy. This is the last chance for judges in the UK to halt this unjust extradition of an innocent man."