U.S. prosecutors are seeking to put Assange, 52, on trial on 18 counts, all bar one under the Espionage Act, over WikiLeaks' high-profile release of confidential U.S. military records and diplomatic cables.
Assange's lawyers in February sought permission to challenge Britain's approval of his extradition.
In their ruling, two senior judges said he had a real prospect of successfully appealing against extradition on a number of grounds.
The court said in its written ruling that Assange arguably would not be entitled to rely on the First Amendment right to free speech as a non-U.S. national and that he could later be charged with a capital offence, meaning it would be unlawful to extradite him.
British ministers "had an explicit statutory obligation not to order the applicant’s extradition if he could be sentenced to death for the offence concerned, or if he could be charged with an extradition offence disclosed by the same facts in respect of which a sentence of death could be imposed," the judges said.
If those assurances are not forthcoming, then Assange will be granted permission to appeal. A further hearing has been scheduled for May 20, meaning his extradition - which his campaign team said could have been imminent depending on the ruling - has been put on hold.
Although Assange's legal team were successful on some grounds, the court rejected his bid to appeal on the basis that the case was politically motivated or that he would not receive a fair trial.
The U.S. says the WikiLeaks' revelations imperilled the lives of their agents and there was no excuse for his criminality.
Assange's many supporters hail him as an anti-establishment hero who is being persecuted, despite being a journalist, for exposing U.S. wrongdoing and alleged war crimes.
The U.S. meanwhile said Assange had been charged for "indiscriminately and knowingly" publishing sources' names and not his political opinions.
