I / London May 28, 2012, 11:13 IST
Britain's highest court is Assange's final avenue of appeal under UK law, having been detained in December 2010 on a European arrest warrant. He is wanted in Sweden for questioning over allegations of rape and sexual assault.
The judgment, expected to take around 10 minutes, will be handed down at 9:15am Wednesday, streamed on the Sky News website and published online once delivered.
Assange has to live under restrictions on his movement for 540 days when the verdict is handed down.
Assange's case rests on a single point -- that the Swedish prosecutor who issued a warrant for his arrest was not a valid judicial authority.
The Supreme Court president will give a summary of the point of law raised by the appeal, the court's decision, and a brief explanation of its rationale.
A lower court in Britain initially approved Assange's extradition to Sweden in February 2011.
An appeal to the High Court was rejected in November, but he subsequently won permission to appeal to the Supreme Court.
If court rejects his appeal, Assange will have exhausted all his options in Britain but he could still make a last-ditch appeal to the European Court of Human Rights in Strasbourg, France.
Assange has said he fears his extradition would eventually lead to his transfer to the United States, where US soldier Bradley Manning is facing a court-martial over accusations that he handed documents to the anti-secrecy website WikiLeaks.
On May 23, Assange attended a screening in London wearing a Kevlar Guy Fawkes mask.
"This may be my last time in public, so I thought I should start with a situation where you won't be able to see me anymore," he explained.
Assange added: "I think all of us are at our best when we are pursuing an ideal that we find to be important to ourselves and important to others.
"I feel that I have made my days count, so I certainly would not want to exchange days that can be counted for days that cannot."
The Supreme Court is the final court of appeal in Britain for civil cases. It hears appeals in criminal cases from England, Wales and Northern Ireland. It also hears cases of the greatest public or constitutional importance affecting the whole population.