A court official confirmed that it had received the request for an appeal, but no date has yet been set for a hearing.
Assange said after last week's ruling that he was prepared for a lengthy legal battle after judge Howard Riddle rejected defence arguments that the 39-year-old would face an unfair trial that would breach his human rights.
The founder of the whistleblowing website claimed that the decision to extradite him was a "result of the European Arrest Warrant system run amok".
He also complained that the hearings to consider Sweden's extradition requests had failed to consider "the merits of the allegations against me".
The latest twist in Assange's fight against extradition comes after US authorities lodged 22 additional charges against Bradley Manning, the US soldier accused of passing a host of confidential documents to WikiLeaks.
The new accusations include the accusation of "aiding the enemy," which carries a potential death sentence.
On Wednesday, the Swedish Bar Association (Advokatsamfundet) summoned Assange's Swedish lawyer Björn Hurtig to answer questions about ethics breach allegations made by Riddle.
Among other things, Riddle accused Hurtig of making a "deliberate attempt to mislead the court."
The judge was referring to testimony in which Hurtig had said he had been unable to contact Assange last year when he was sought by Swedish prosecutors for questioning.
Hurtig himself told the TT news agency Wednesday that he was "eager to explain himself," although he stressed he felt he had "already explained my error when I changed my statement in front of the court."
He has until March 14th to respond to the bar association's questions.