The cyclist received the prestigious award after winning tonight's public phone vote, beating Jessica Ennis and Andy Murray into second and third place respectively.
The prize was presented by David Beckham and the Duchess of Cambridge, in her first appearance since visiting hospital with acute morning sickness.
"I'm not going to swear tonight, so I'm just going to say thanks very much to everyone who picked the phone up and voted," Wiggins said.
"We've had all that jungle stuff and The X Factor the last couple of weeks so, for people, in half an hour, to pick up and pay £1.50 to vote, thank you very much.
"I'd like to thank my teammates because without them I wouldn't be here tonight."
Wiggins's fellow nominees included runner Mo Farah, rower Katherine Grainger, boxer Nicola Adams, sailor Ben Ainslie and cyclist Sir Chris Hoy.
Paralympians Sarah Storey, Ellie Simmonds and David Weir and golfer Rory McIlroy also made the shortlist for the ceremony, which took place at the ExCel Centre in London.
Other awards handed out tonight included Young Sports Personality of the Year, which went to 15-year-old Paralympic swimmer Josef Craig. Lord Sebastian Coe won the Lifetime Achievement Award.
Digital Spy readers had backed Wiggins to win Sports Personality of the Year 2012, with 23.4% of the vote.
Photo gallery - BBC Sports Personality of the Year 2012: