Assange's lawyers said immediately they planned to appeal against the decision to London's High Court and it could still be months before the legal process in Britain reaches an end.
The 39-year-old Australian computer expert remains in Britain on bail in the meantime.
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.
Judge Howard Riddle dismissed Assange's arguments that he could not get a fair trial in Sweden and said extradition to Sweden would not violate his human rights.
"I must order Mr Assange be extradited to Sweden," he told London's top-security Belmarsh Magistrates' Court in a case covered by scores of reporters from around the world.
About a dozen Assange supporters, wearing masks and costumes or Guantanamo Bay-style orange boiler suits, chanted in front of the courthouse.
Reuters
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