Cavendish exploded across the line in a bunch sprint, ahead of Australia's Matt Goss and German Andre Greipel.
"It was incredible, we took it on from start to finish," said Cavendish.
"I can't believe it. We knew three years ago when this course was announced - we put a plan together to put these best guys together.
"It's been three years in the making and you just saw they rode incredibly. I'm just so proud.
"The biggest goal next year [is the Olympics] and I hope we can make it a world and Olympic double."
The 26-year-old's victory is the first world road race success for a British man since Tom Simpson won gold in 1965.
Cavendish is also the first rider since Belgium's Freddy Maertens, 30 years ago, to win both this race and the Tour de France green jersey in the same year.
His team, guided strategically by David Millar in the absence of radio communication, spent much of the race playing a restrained waiting game as all kinds of attacks developed around them.
Cavendish thanks 'amazing' GB team
An early seven-man break settled into an advantage of around seven minutes around the flat Copenhagen course in the opening 100km, with Britain, chiefly Chris Froome, leading the chasing bunch.
Belgium's Johan van Summeren led a separate five-man group clear of the peloton at the 150km mark as the race kicked to life earlier than many had expected.
A crash in a narrow portion of the course involving France's Blel Kadri caused further havoc, leaving some 20 riders - among them Frank Schleck and defending world champion Thor Hushovd - temporarily trapped as service cars and mechanics struggled to reach them.
Born 21 May 1985
on the Isle of Man, for whom he competes at the Commonwealth Games
First major cycling title
was madison gold on the track at 2005 World Championships, alongside Rob Hayles
Began road racing
in 2005 and made his Tour de France debut in 2007
Won a Tour de France stage
for the first time in 2008. He now has 20 stage wins, placing him sixth on the all-time list
The only track cyclist
to return from Beijing 2008 without a medal, finishing ninth in the madison
Won Tour de France green points jersey
, traditionally dominated by sprinters, in 2011 (above)
As the race progressed at a fierce pace, Britain's tactics became clear: a reluctance to get riders into the moves being made off the fractured front of the group, in favour of an ambition to control proceedings throughout.
Few other nations saw fit to help their watching brief, and GB found themselves policing the peloton - hauling it forward and keeping it together - for almost the entire race.
The breakaway evaporated inside two laps from the finish while Froome, Steve Cummings and Jeremy Hunt fell away from the British train after expending vast sums of energy earlier in the race.
Bradley Wiggins, the world time trial silver medallist earlier this week, produced a superb stint at the front before handing to Ian Stannard and Geraint Thomas for the very closing stages.
Thomas threw a panicked look behind him as Cavendish looked in danger of becoming boxed-in as they reached the finishing straight.
But the Manxman accelerated away in trademark style on the right-hand edge of the pack to secure victory.
"At the start of the season I said I had two goals: the green jersey and the rainbow stripes," said Cavendish. "Now I get to wear the rainbow bands for the next year.
"The team all rode out of their skins today. It's a shame they can't wear the world champion's jersey as well. I've won the jersey, but I just put the finishing touches to the mission.
"The Olympics is different, because you've only got five riders and the course next year will be more difficult than here.
"But I'm going to prepare as best as I can for it."
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