"The Supreme Court has granted permission to appeal and a hearing has been scheduled for two days, beginning on 1 February 2012," said a statement from the Supreme Court, the highest court in England.
The decision means Assange will spend a second Christmas at the country mansion of a wealthy supporter in Norfolk, eastern England.
He was arrested last December on a European arrest warrant issued by Sweden after allegations by two women of sexual assault and rape.
The 40-year-old Australian strongly denies any wrongdoing and says the sex with the women was consensual.
He believes the allegations are politically motivated and linked to WikiLeaks' release of hundreds of thousands of classified US files about the wars in Iraq and Afghanistan.
The Supreme Court decision comes as Bradley Manning, the US soldier accused of passing the files to WikiLeaks, is due to make his first appearance in a US court on Friday.
The hearing will determine whether the former intelligence analyst, who turns 24 on Saturday, should be tried on charges which could see him sentenced to life imprisonment.
Manning is accused of downloading 260,000 US diplomatic cables, videos of US air strikes and US military reports from Afghanistan and Iraq between November 2009 and May 2010 while serving in Iraq, and transferring them to WikiLeaks.
US Secretary of State Hillary Clinton, speaking on the eve of Manning's hearing, said it was a "very unfortunate and damaging action... that put at risk individuals and relationships."
Manning's supporters say his health has sharply deteriorated while in custody.