England were all out for 353 on the final day at the WACA Ground to hand the home side an unbeatable 3-0 lead in the five-match series.
It capped a remarkable turnaround for Australia, who went into the series just months after a 3-0 Ashes loss in England.
"I don't really know what to say. We've got them back, I couldn't be happier," Clarke said of the Ashes, which England had held for the past three series.
Despite a determined rearguard action -- led by rookie English batsman Ben Stokes, whose maiden Test century frayed Australian nerves -- the home team ran through the English tail after lunch to claim a famous victory.
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The Australians had won the first two Tests in Brisbane and Adelaide and secured the urn when rejuvenated paceman Mitchell Johnson claimed his 23rd wicket of the series to remove Jimmy Anderson and end the England second innings.
Although the Ashes have been regained, Clarke said Australia were targeting a 5-0 win in the series as they seek to climb from fifth in the world Test cricket rankings.
England captain Alastair Cook praised the character of Stokes and admitted the English were starting to dream of the impossible, but added that the result reflected the series.
"Just when we got a partnership going, we haven't managed to turn it into big one," he said.
"We have been outskilled in all aspects, and it is hard to say that. They have been ruthless. It hurts."
Set a record 504 to win, England went to lunch on the final day at 332-6, needing 172 more runs with four wickets in hand and Stokes still at the crease.