Two High Court judges rejected Assange's claim his extradition would be "unfair and unlawful," the Financial Times reported.
Assange has two weeks to appeal to the British supreme court.
A "Free Assange" rally was planned for outside the Royal Courts of Justice in London, CNN reported.
Assange's lawyers had argued the European arrest warrant wasn't valid and the allege offenses wouldn't be considered crimes in Britain.
Swedish authorities won their extradition case in February but Assange appealed in July. Assange has been living in Britain under house arrest since December.
He maintained he is innocent of allegations made by two Swedish women he engaged in "non-consensual, coerced" sex and that the charges are part of a smear campaign. British prosecutor Clare Montgomery, representing the Swedish prosecutors, argued in July the two women were "trapped into a position where they had no choice."
The whistle-blowing WikiLeaks, which published hundreds of thousands of U.S. diplomatic and military communications last year, recently stopped publishing to focus on fundraising. Assange said the site must raise $3.4 million before year's end to maintain operations because of "an arbitrary and unlawful financial blockade" by the Bank of America, Visa, MasterCard, PayPal and Western Union.