Assange's lawyers have a week to appeal. Assange has been out on bail during the extradition fight.
Assange has not been charged, but Swedish prosecutors want to question him about accusations of sexual abuse being made by two women.
Judge Howard Riddle said that "there is simply no reason to believe there has been a mistake" about Assange's arrest warrant.
The defendant's lawyers have argued that Assange won't get a fair trial because of his notoriety and because rape cases in Sweden are customarily held without the public present. Sweden contends its trials are fair.
The lawyers also expressed concern their client risks being handed over to the U.S., which is still investigating whether Assange's secret-spilling website should be held responsible for leaking thousands of classified documents.
The Associated Press contributed to this report.