An extradition order was issued by chief magistrate Paul Goldspring during a seven-minute hearing at Westminster Magistrates’ Court on Wednesday.
Mr Goldspring said: “In layman’s terms, I am duty bound to send your case to the Secretary of State for a decision.”
Outside the court, scores of supporters gathered carrying placards reading “Don’t extradite Assange”.
The extradition may yet be further delayed by an appeal.
Assange, 50, was not present in court physically, although he watched the administrative proceedings by video link.
He is wanted in America over an alleged conspiracy to obtain and disclose national defence information following WikiLeaks’ publication of hundreds of thousands of leaked documents relating to the Afghanistan and Iraq wars.
His legal team claimed the publication of classified documents exposed US wrongdoing and were in the public interest.
They said the prosecution was politically motivated and that he faces up to 175 years in jail.
Assange, who married his fiancee Stella Moris last month, has been held in Belmarsh prison for three years since being dragged out of the Ecuadorian embassy in London.
Mrs Assange was in the public gallery for the hearing.