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.
"Credit to the team for how they played: they were outstanding."
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.
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.
"We want to get back that number one ranking," he said.
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.
However, Australia turned the screws when spinner Nathan Lyon (3-70) picked up the wicket of Stokes for 120 in the third over after the break.
Stokes, who scored the first English century of the series in just his second Test, attempted to sweep a ball outside off stump and got a thin bottom edge, with wicketkeeper Brad Haddin continuing his outstanding series by hanging on to a diving catch.
It was the end of a superb knock by Stokes, who showed up his more senior teammates by staying at the crease for 257 minutes and facing 195 balls, hitting 18 fours and one six.
His departure also ended a 40-run partnership with Tim Bresnan.
Lyon then picked up Graeme Swann for four, caught at short leg, as Australia closed in on victory.
Bresnan (12) was the next to go, brilliantly caught by a diving Chris Rogers at mid-off from the bowling of England's chief nemesis Johnson as celebrations by local fans went into full swing.
The match was over when Johnson (4-78) claimed his final scalp of the innings, with Anderson caught at short leg by George Bailey.
England had resumed on 251-5, but Stokes defied the Australian attack for the entire morning session, losing only Matt Prior (26) along the way.
Stokes, 22, was temporarily denied a century when he drove Johnson straight and the ball deflected off the bowler's hand into umpire Marais Erasmus, costing him the two runs he needed to reach the milestone.
But he got a top edge to fine leg for a boundary from the next ball to notch his first Test century.
Not for the first time in the series, it was Johnson who delivered a dagger to English hearts by removing Prior in his third over with the second new ball, ending a 76-run partnership with Stokes.
Australia 1st innings 385 (Steve Smith 111; Stuart Broad 3-100)
England 1st innings 251 (Alastair Cook 72; Peter Siddle 3-36)
Australia 2nd innings 369-6 (dec) (David Warner 112, Shane Watson 103; Tim Bresnan 2-53)
England 2nd innings
Alastair Cook b Harris 0
Michael Carberry lbw Watson 31
Joe Root c Haddin b Johnson 19
Kevin Pietersen c Harris b Lyon 45
Ian Bell c Haddin b Siddle 60
Ben Stokes c Haddin b Lyon 120
Matt Prior c Haddin b Johnson 26
Tim Bresnan c Rogers b Lyon 12
Graeme Swann c Smith b Lyon 4
Stuart Broad not out 2
Jimmy Anderson c Bailey b Johnson 2
Extras (b13, lb13, w6) 32
Total (all out wickets, 103.2 overs) 353
Fall of wickets: 1-0 (Cook), 2-62 (Carberry), 3-76 (Root), 4-121 (Pietersen), 5-220 (Bell), 6-296 (Prior), 7-336 (Stokes), 8-347 (Swann), 9-349 (Bresnan), 10-353 (Anderson).
Bowling: Harris 19-2-73-1, Johnson 25.2-6-78-4 (5w), Lyon 22-5-70-3 (1w), Siddle 26-11-67-1, Watson 11-1-39-1.
Australia won by 150 runs
Australia leads series 3-0
Umpires: Marais Erasmus (RSA), Billy Bowden (NZL)
TV umpire: Tony Hill (NZL)
Match referee: Jeff Crowe (NZL)