The BBC award winner, dressed in a navy velvet suit, said he had been a fan of the Sports Personality show since he was a child.
"Sports Personality is a bit of an institution in our house and always has been. To win this it's very difficult to put into words," he said after receiving the award from the Duchess of Cambridge.
"It's incredible, and I'm very proud. It's something I certainly wanted to win."
Team Sky rider Wiggins said he would have voted for Paralympic wheelchair racer David Weir and was "starstruck" when he met him.
Wiggins teases 'Susan' Barker
"The 12 nominees all achieved things in their own right. It was probably the most nerve-wracking thing of the year for me," said the first English winner since Zara Phillips in 2006.
"I was inspired as a 12-year-old watching [Olympic gold medallist and Tour stage winner] Chris Boardman and hopefully this year will have done the same for others."
Wiggins, who was born in Belgium, grew up in London and is now based in Lancashire, said he would let his grandmother have the trophy before putting it behind the bar at his local pub - the
Farmers Arms in Eccleston.
He won his fourth career title, and a British record seventh medal, at the Olympics and London 2012 chief Lord Coe - himself the recipient of a lifetime achievement award - hailed sport's "rock star".
"He's more than just a fantastic ambassador. He's edgy and got that slightly risky feel to him," said Coe.
At the after-show party, Wiggins joined the house band on stage as he played guitar to songs by The Jam and Oasis.
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