Swedish authorities want to question the 40-year-old Australian over accusations of rape and sexual assault made by two female former WikiLeaks volunteers in August 2010.
Assange, who has been living in Britain since his arrest here in December last year, denies wrongdoing.
He now has 14 days in which to formally lodge an appeal, meaning his stay in Britain is certain to stretch into 2012.
Assange spent nine days in London’s Wandsworth prison after his arrest last year. He was freed a week before Christmas on bail and has since been living at the country house of a wealthy supporter in eastern England.
His arrest came shortly after WikiLeaks published thousands of secret U.S. diplomatic cables that included unflattering views of world leaders and candid assessments of security threats.
Assange says the allegations are politically motivated.
He had lost his last attempt to avoid being sent to Sweden on Nov. 2 after two High Court judges upheld a previous ruling.
In 2010, WikiLeaks posted 391,832 secret papers on the Iraq war and 77,000 classified Pentagon documents on the Afghan conflict. It has also made available about 250,000 individual cables, daily traffic between the State Department and more than 270 American diplomatic outposts around the world.