The victory gave Australia an unbeatable 3-0 lead in the five-Test series, with two Tests, in Melbourne and Sydney, remaining.
There were jubilant scenes here on Monday as the Australians atoned for losing the Ashes 2-1 in England in 2005.
Set an unlikely 557 to win after Australia declared at 527 for five late on the third day, England looked to have some hope of at least saving the match, and the series, when they were 336 for five shortly before lunch on the last day, with both Kevin Pietersen and Andrew Flintoff at the wicket.
However, champion leg-spinner Shane Warne once again struck with telling impact, bowling Flintoff for 51 to spark an English collapse that saw them lose their last five wickets for just 14 runs.
Warne ultimately ended the resistance two balls after lunch when he bowled Monty Panesar for one, with England all out for 350.
Warne claimed 4-115 from 39.2 overs in the England second innings to take his career tally to 699 Test wickets and he now looks certain to become the first bowler to reach 700 Test wickets in front of his home crowd at the MCG in the fourth Test starting December 26.
The loss of opener Alastair Cook and nightwatchman Matthew Hoggard in the last three overs of the fourth day's play had rocked England's hopes of saving, or even winning, the Test.
However, Pietersen (60 not out) and Flintoff started the final day with intent, the latter bursting out of a form slump with some aggressive shots as they built a partnership before lunch.
Although he lived dangerously at times, Flintoff hit a string of boundaries and a big six over mid-wicket off the bowling of Brett Lee.
He reached his half-century with an inside edge to the fine-leg boundary, before he played all around a fullish delivery from Warne and was clean bowled to end a 75-run stand.
It proved to be the end of the England resistance, with three more wickets falling in quick succession before the lunch break, which came with Australia needing just one more wicket to win.
Struggling wicketkeeper Geraint Jones surely handed his Test spot to understudy Chris Read when he went in bizarre circumstances for a duck shortly after Flintoff fell.
Jones missed with an attempted sweep at Warne and forgot to get back into his crease, with Australian captain Ricky Ponting hitting the stumps with an underarm throw from silly mid-off.
It completed a pair for Jones and extended his run of ducks on tour to four.
Sajid Mahmood's miserable recall continued when he was adjudged lbw to Stuart Clark (2-56) for just four, while Steve Harmison was trapped lbw by Warne for a duck.
The England tail had wagged strongly on the second day, but there was to be no repeat.
In the end, the English fought desperately hard but blew their opportunity to stay in the series when their top order failed to fire on the second day of the game.
After dismissing Australia, who had won the toss and elected to bat, for just 244, England slumped to 128 for seven before being dismissed for 215.
Centuries to Adam Gilchrist, who hit the second fastest Test hundred in history, Mike Hussey and Michael Clarke then put the home side in a commanding position.
Although Alastair Cook held the Australians at bay with a fighting century, the English had missed their chance.
Australia 244 and 527 for 5 decl beat England 215 and 350 (A Cook 116, Ian Bell 87, Kevin Pietersen 60 n o, Andrew Flintoff 51; Warne 4 for 115, Clark 2 for 56, McGrath 2 for 61)
Result: Australia beat England by 206 runs to regain Ashes after winning the Brisbane and Adelaide Tests.