The motion, moved by independent lawmaker Andrew Wilkie, was passed on Wednesday with 86 votes in favour and 42 against after it was supported by the Labor government.
"(The motion) will send a powerful political signal to the British government and to the U.S. government," Wilkie told parliament ahead of the vote.
Assange's supporters say he has been victimised because he exposed U.S. wrongdoing and potential crimes, including in conflicts in Afghanistan and Iraq.
Washington says the release of the secret documents put lives in danger.
Australia's Attorney-General Mark Dreyfus said Assange's extradition was raised in a meeting with his U.S. counterpart Merrick Garland in Washington last month.
Persons:
Renju Jose SYDNEY, Anthony Albanese, Julian Assange, Andrew Wilkie, Wilkie, Assange, Albanese, Mark Dreyfus, Merrick Garland, Dreyfus, Renju Jose, Jamie Freed
Organizations:
Australia's, WikiLeaks, London's, Labor, ., Britain, Australian Broadcasting Corp, U.S
Locations:
Australia, United States, Australian, Britain, Afghanistan, Iraq, Washington, Sydney