Judge Howard Riddle says the allegations of rape and sexual molestation by two women are extraditable offenses and a Swedish warrant was properly issued.
Lawyers for Assange have a week to appeal Thursday's decision.
Riddle says "there is simply no reason to believe there has been a mistake" in issuing the warrant.
Assange has been out on bail during the extradition fight.
His lawyers have questioned Sweden's judicial process and expressed concern their client risks being handed over to the U.S., which is investigating whether Assange's website should be held responsible for leaking classified information.
Lawyers for Sweden have argued that authorities made repeated attempts to interview Assange while he was in Scandinavia, but to no avail.