British Home Secretary Priti Patel approved the extradition of the WikiLeaks founder in June after he was denied an appeal in the Supreme Court appeal back in March.
A public relations firm representing Assange said in a statement that the respondents to the appeal were Ms Patel and the government of the United States.
Lawyers for Assange will argue that he is being prosecuted and punished for his political opinions and for protected speech, and that the extradition request violates the US-UK Extradition Treaty and international law as it relates to what it calls political offences.