The gymnast group wowed the reality show's judges and were hailed by Simon Cowell as the "most astonishing" thing he has seen on live television.
Spelbound, who were the bookies' favourites for success – more than 1 million was wagered on the result – secured the public vote with a routine involving one of the dancers being launched over judge Amanda Holden.
Cowell added: "The show is called Britain's Got Talent and absolutely the right guys and girls won on the night."
One of the finalists they beat was Scottish great-granny Janey Cutler, from Wishaw, Lanarkshire, who has been this year's singing surprise and was hailed as the new Susan Boyle.
But the 81-year-old was eclipsed by Spelbound, an acrobatic group from Ashford, Middlesex, who took the 100,000 prize and will perform at the Royal Variety Performance.
Spelbound's coach Neil Griffiths said: "This is just a dream come true. They have worked so hard over the last few weeks. We pulled out all the stops for the final and on Friday they rehearsed from 6am to midnight."
Cutler did not even make the final three according to the public vote, with second place going to dance duo Twist and Pulse, from London.
In third place was 13-year-old drummer Kieran Gaffney, from Kent.
After watching the scantily-clad Spelbound perform to the soundtrack of Carmina Burana, the judges queued up to pay tribute to the act.
Piers Morgan said the purpose of the show was to unearth hidden gems and added: "You are that talent."
Holden added: "We are hosting the Olympics Games and I can only think, what a brilliant opening act."
Dancing dog Chandi failed to wow the judges as much as she had in previous rounds as her owner, Tina Humphrey, 37, was forced to claim "there's life in the old dog".
After performing a version of Let's Face The Music And Dance, Cowell said: "She's a special dog and in human years she is about 100."
But, to boos from the audience, he added: "She is looking a bit tired I think."
Drummer Kieran had the judges singing his praises after performing on his set while elevated from the ceiling. Cowell added: "If it was your idea, and it was, it shows what a clever young man you are. You are a showman."
Cutler, the singing grandmother, got off to a difficult start as she sung Edith Piaf's No Regrets.
But Cowell said supporters should overlook a stuttering start to her routine, adding: "What you have got to do is forget the first part and listen to the second."
Twist and Pulse were first to perform with their medley of fast-pace moves.
Morgan said of the pair: "Sometimes people say it's a disadvantage to go first in the final because people won't remember.
"Well I think in this case it's been a massive advantage to you two because you have set the bar tonight for the others to follow."
Child crooner Liam McNally sang Danny Boy and was praised for being "note perfect" by Cowell, while Paul Burling was dubbed "really, really funny and inventive" for his combination of impressions before the audience.
Despite being written off by many critics, Tobias Mead gave himself a shout of winning as he breakdanced backwards to wow the critics.
Morgan said Mead was a "showman" who could perform in Las Vegas.
Cherubic schoolboy band Connected sang Westlife's What About Love.
The judges said the band would be "massive" but their hopes appeared dashed after Cowell said their song choice was bad.
A special guest performance by Usher helped extend the show to two-and-a-half hours while the public voted for their favourite act.
The show also debuted the World Cup song Shout by comedian James Corden and Dizzee Rascal in front of a wild mob of England fans on stage.
Spelbound is made up of Adam McAssey, 20, Adam Buckingham, 21, Alex Uttley, 24, Jonathan Stranks, 15, Douglas Fordyce, 19, Edward Upcott, 18, Nicholas Illingworth, 24, Katie Axten, 17, Leighanne Cowler, 18, Lauren Kemp, 17, Hollianne Wood, 13, Abigail Ralph, 15, and Amy Mackenzie, 12.