Swedish prosecutors want to question Assange about allegations of sexual misconduct, which he denies, made by two WikiLeaks volunteers during his time in Sweden last August.
One alleges Assange, who has angered the US government by releasing thousands of secret US diplomatic cables on his website, sexually molested her by ignoring her request for him to use a condom during sex.
The second woman has said Assange had sex with her while she was asleep and that he was not wearing a condom.
Prosecutors say the second allegation falls into the least severe of three categories of rape in Sweden, carrying a maximum of four years in jail.
During three days of legal argument earlier this month, lawyers for Assange argued he would not get a fair trial in Sweden and said Swedish prosecutors had mishandled the case against the 39-year-old Australian computer expert.
They argued that he might wind up being sent to the United States where he could face execution.
Assange's lawyers also accused Sweden's Prime Minister Fredrik Reinfeldt of creating a "toxic atmosphere" in Sweden and damaging his chances of a fair trial by portraying him as "public enemy number one".
However, Judge Howard Riddle dismissed the arguments and ordered Assange be extradited although his lawyer said they would appeal against the decision.
The Swedish prosecution authority had no immediate comment but would post a statement on its website shortly, a spokeswoman for the office said.
Extradition order 'gang rape'
The mother of Julian Assange condemned the court’s extradition order as "political and legal gang rape", the Australian Associated Press reported.
"I would say that what we're looking at here is political and legal gang rape of my son," AAP quoted Christine Assange as saying.
"It's a real David and Goliath situation," she said.
"You've got misuse of the European arrest warrant, first time ever that it's been used this way."
"What Julian through his site is proving (is) the need for WikiLeaks," his mother said. "I'm, obviously, scared for him as a mother but the world ought to be scared for its democracies."
She said that she had expected the extradition order, and that her son felt abandoned by the Australian government.
"The greatest fear I have is that the Western world in its effort to shut up someone who's telling the truth to the people of their countries will breach every piece of legislation in order to get him and will co-operate across borders to do so."
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