Michael Clarke's side had gone into the final without a loss in the Caribbean tournament but were never in the hunt after losing 3-8 in the first 2.1 overs.
England captain Paul Collingwood said beating arch-rivals Australia final was "right up there" with winning the Ashes.
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Collingwood, leading the team because Test captain Andrew Strauss has opted out of Twenty20 cricket, was a member of the England sides that won the 2005 and 2009 Ashes series.
And, having hit the winning runs on Sunday, he was in no doubt about the importance of this victory which ended a run of four defeats in major finals for England (the 1979, 1987 and 1992 World Cups and the 2004 Champions Trophy).
"It's right up there, it's got to be," he said at the presentation ceremony.
England 'full of confidence'
"This is our first World Cup we've ever won and the boys deserve it.
"We've got some good players in the side, the work ethic we've had over the past year and we're starting to see the results on the pitch," Collingwood said.
"There's a lot of confidence in the side; you can see the belief that we've got going out on the pitch. The power that we've got, the thought processes the bowlers are using, the fielding, everything seems to be stronger."
David Hussey played a determined innings of 59 to lead Australia's recovery for a total of 6-147 but England were untroubled, reaching 3-151 in 17 overs.
South African-born duo Kevin Pietersen (47) and Craig Kieswetter (63) added 117 for England's second wicket in a match-winning partnership.
Kieswetter was named man of the match and Pietersen, who missed a game during the tournament to attend the birth of his son in London, was player of the series with 248 runs at an average of 62.00.
'Beaten by a better team'
"Losing those three wickets early certainly didn't help us and put a lot of pressure on our middle order," Clarke said.
"But we did well to scrape to 140-odd. In the end we were probably 30 runs short. But in saying that, the way England came out and batted we were probably 50 runs short.
"That's the way it goes. We got beaten by a better team today."
After Shaun Tait removed Michael Lumb (2) in the second over, leg-spinner Steven Smith and left-armer Mitchell Johnson dismissed Pietersen and Kieswetter in the 14th and 15th overs.
But England settled with skipper Paul Collingwood unbeaten on 12 including the winning boundary and Eoin Morgan 15 not out.
Collingwood had invited Australia to bat first and left-armer Ryan Sidebottom (2-26) claimed Shane Watson (2) and Brad Haddin (1) while David Warner (2) was run out.
Hussey dropped by Broad
Clarke (27) chipped a catch to rival skipper Paul Collingwood at 4-45 in the 10th over.
Cameron White crunched 30 from 19 balls, adding 50 in a crucial fifth-wicket partnership with David Hussey who was dropped by Stuart Broad at mid-wicket on 25.
David Hussey's 54-ball knock included two fours and two sixes.
The right-hander was run out in the final over after a 47-run partnership with brother Mike who was unbeaten on 17.
Spinner Graeme Swann was economical with 1-17 from his four overs.
Australia would take little comfort in the fact this was a step forward for the team after failing to reach the final in two previous World T20 events.
Haddin fined for dissent
It's England's first win in a major limited-overs trophy event, after making the decider in the Champions Trophy once and the World Cup three times.
The ICC later announced Australia wicketkeeper-batsman Brad Haddin had been fined 10 per cent of his match fee for a violation of the Code of Conduct.
Haddin pleaded guilty to a charge of showing dissent after an umpire's decision.
The batsman was given out caught behind down leg-side for one off the bowling of paceman Ryan Sidebottom.
But the ball appeared to miss the bat and strike Haddin on the hip and the Australian stood at his crease and pointed to his hip after being dismissed.
