A panel of seven Supreme Court justices will hear the appeal -- a high number, the court said in a statement, because of the "great public importance of the issue," The Guardian reported.
In a two-day hearing to begin Feb. 1, justices will weigh whether a Swedish prosecutor is a "judicial authority" with the power to extradite the Australian-born Assange.
His lawyer has argued public prosecutors are not judicial authorities and therefore do not have the power to issue warrants under extradition law, making the warrant invalid.
If Assange loses the appeal, he may still be able to challenge the extradition in the European Court of Human Rights in Strasbourg, France.
Assange, 40, has been held on allegations he raped one woman and sexually assaulted another during a visit to Sweden in August 2010.
He has denied wrongdoing, saying the sex was consensual and calling the case against him politically motivated because he operates WikiLeaks, which reveals secret information about governments throughout the world.