STORY: Patel gave the go-ahead for the extradition on Friday but Wikileaks and his wife, Stella Assange, said he would appeal the decision.
"We were preparing for this situation and our fighting spirits are even stronger than before, and Julian is ready to appeal this decision and fight on," she told Reuters following a news conference.
Assange's lawyer Jennifer Robinson told Reuters his case would be taken to the European Court of Human Rights if the appeal was not successful in the UK.
Robinson also called on the Australian government to step in and put pressure on U.S. President Joe Biden over the Australian citizen's case.
The Australian government said it would continue to tell London and Washington that the case had "dragged on for too long and should be brought to a close."
Assange is wanted by U.S. authorities on 18 counts, including a spying charge, relating to WikiLeaks' release of vast troves of confidential U.S. military records and diplomatic cables which Washington said had put lives in danger.
His supporters say he is an anti-establishment hero who has been victimised because he exposed U.S. wrongdoing in conflicts in Afghanistan and Iraq, and that his prosecution is a politically motivated assault on journalism and free speech.