Speaking at London's Excel Centre as he accepted the award, Bradley Wiggins said: "What a year, and to stand on this stage with the likes of these people next to me is incredible.
"And I'd like to thank my team mates because again without them I wouldn't be here tonight, and wouldn't be stood on this stage... To all the Olympians here tonight, because again it would be nothing stood here without the incredible year that we've had, so thanks to everyone."
Wiggins won the public vote after becoming the first Briton to win the Tour de France, cycling's ultimate prize, in July, followed days later by the Olympic Time Trial on the streets of Surrey.
Team GB Heptathlon gold medal-winner Jessica Ennis was second, with US Open tennis winner and Olympic gold medallist Andy Murray third.
Tour de France winner and Olympic gold medallist Bradley Wiggins has won the Sports Personality of the Year award.
The Duchess of Cambridge presented Lord Sebastian Coe with the Lifetime Achievement award in her first public engagement since leaving hospital for severe pregnancy sickness.
Roger Mosey, the Acting Director of BBC Television, tweeted to say that the Duchess of Cambridge has arrived at the Excel Centre where she will present the Sports Personality of the Year and Lifetime Achievement awards.
Martine Wright, who lost her legs in the London bombings on July 7, 2005, and competed in the sitting volleyball at the 2012 Paralympics, won the Helen Rollason Award.
This is presented in memory of the BBC presenter who died in 1999 at the age of 43 after suffering from cancer, and is given for outstanding achievement in the face of adversity.
Wright said: "I am absolutely honoured to be here. I count myself lucky to have survived that awful day, and that I've made an incredible journey, the last seven years."
She thanked the emergency services and medical staff who did so much and added that she "will never forget the 52 people that sadly lost their lives, so this is definitely for them as well."
Josef Craig, Britain's youngest gold medallist of London 2012, scooped the Young Sports Personality of the Year award.
Craig won the S7 400 metres freestyle at the Paralympics at the age of just 15.
Paralympic gold medallist Sarah Storey revealed that she is 13 weeks pregnant today and is expecting a baby on June 23. Storey, who is nominated for Sports Personality of the Year, said it was "an absolute honour" to be shortlisted for the award.
Olympic gold medallist Jessica Ennis told ITV News it was "exciting to be in the top 12" for Sports Personality of the Year.