That made him a hero to anti-censorship campaigners. But Washington was furious about the release of classified documents.
Assange was not present at the court hearing but WikiLeaks spokesman Kristinn Hrafnsson said he saw Washington's hand in the ruling. "This is not the final outcome. What we have here is retribution from the U.S.," he said.
Assange has faced widespread criticism that he put lives at risk by blowing the cover of sources who spoke to diplomats and intelligence agents in countries where it was dangerous to do so.
WikiLeaks has since faded from the headlines due to a dearth of scoops and a blockade by credit card companies that has made donations to the site almost impossible. Assange's personal standing has been damaged by the Swedish sex case and he has lost support from most of his celebrity backers.
Since his detention, he has mostly been living under strict bail conditions at the country mansion of a wealthy supporter in eastern England. His associates say that amounts to 540 days under house arrest without charge.
Assange's appeal hinges on a legal technicality rather than the substance of the allegations of sexual misconduct or his claims that the United States has been putting pressure on Britain and Sweden to take action against him.
His lawyers argued the European Arrest Warrant (EAW) was invalid because it was issued by a prosecutor and not a judge or a court as required in Britain. Prosecutors acting for Sweden say different countries have different legal procedures which are allowable under the agreed EAW format.
EUROPEAN APPEAL POSSIBLE
After Wednesday's ruling the Supreme Court gave Assange two weeks to seek to re-open the case. Assange's lawyers said some of the judges appeared to have based their decision on a legal point that had not been argued in court, preventing them from making a counter-submission.