No date has been set for a hearing in the High Court, challenging the ruling at Belmarsh Magistrates Court.
The 39-year-old Australian who denies the allegations, had said he would appeal if he did not overturn the European arrest warrant at the first attempt.
He faces being sent to Sweden within 10 days if unsuccessful.
Lawyers for Assange filed the appeal against his extradition to Sweden yesterday. The appeal process is likely to last for months as the WikiLeaks founder remains on bail, living under curfew in a rural mansion in eastern England.
On February 24, a British court ordered that Assange be extradited to Sweden for questioning over rape and sexual assault allegations after dismissing claims he will not receive a fair trial there.
Describing the Magistrates court`s decision as a "rubber-stamping process", Assange said last week: "There was no consideration during this entire process as to the merit of the allegations made against me, no consideration or examination even of the complaints made in Sweden and, of course, we have always known we would appeal."
Assange has been fighting extradition since he was arrested and bailed in December and has denied the allegations, made by two women last August.
According to The Guardian, Assange fears removal to Sweden will make it easier for Washington to extradite him to the US on possible charges relating to the release on the WikiLeaks website of US embassy cables.
He believes the claims of sexual assault and rape are politically motivated because of WikiLeaks` publication of sensitive material--including leaked US diplomatic cables--from governments and high-profile organisations that has made headlines worldwide.
Assange has been in the international spotlight for months, since his whistle-blowing website released thousands of US government documents on the wars in Afghanistan and Iraq and on American diplomatic communications around the world.