Chasing 504, England were bowled out for 353 in 103.2 overs to hand back the famous urn to the hosts at the WACA ground on Tuesday.
Australia have taken an unassailable 3-0 lead in the five-match series. The fourth Test begins in Melbourne on December 26.
England had held the Ashes after winning three successive series. They had been the holders since August 23, 2009. It was the the English team for 1,577 days.
The visitors fought hard on the fifth and final day today. Left-hander Ben Stokes (120) led the fightback with his maiden Test hundred. But Australia bowlers were patient throughout and wrapped up the innings in the 104th over.
Mitchell Johnson dismissed last man James Anderson (caught by George Bailey) to trigger celebrations among the players and the crowd in the post-lunch session.
Left-arm quick Johnson was the star for Australia in the series with 23 wickets. In this innings he took 4/78 in 25.2 overs.
"It is a fantastic feeling (to reclaim the Ashes," said a jubilant Australia captain Michael Clarke.
"No doubt, Mitch (Mitchell Johnson) deserves a lot of credit but it has been a team performance over the last three matches," he added.