The 32-year-old made history when he crossed the finish line on the Champs-Elysees and became the first Briton ever to win the most prestigious cycle race in the world.
While fellow Brit Mark Cavendish won the last stage of the 2,173 mile race, Wiggins finished the last day a total of three minutes and 21 seconds ahead of his Team Sky colleague Chris Froome, who became the second British man to make it on to the podium in the race's 99-year history.
The final stage in the French capital was also the 13th consecutive day Wiggins had worn the race leader's yellow jersey
He told ITV: 'Job done really. I don't know what to say really. I've had 24 hours for it to sort of soak in. Today we were just on a mission to finish the job off.
'This sort of thing happens to other people, you never imagine it happens to you. It's incredible.'
There were jubilant scenes when Wiggins stepped up on to the podium and waved to fans while English opera star Lesley Garrett, who was wearing a Union flag as a skirt, sang God Save The Queen.
Wiggins apologised to the French viewers for speaking in English and then addressed the crowds, saying: 'I just wanted to say thank you for all the support all the way around. It's been a magical couple of weeks for the team and for British cycling.
'Some dreams can come true, and now my old mother over there, her son's won the Tour de France.'
London mayor Boris Johnson said: 'Huge congratulations must go to Bradley Wiggins. His incredible determination, focus and will to win blew away the rest of the field and propelled this legendary Londoner to the summit of his sport.'
Allen Reveals Struggle For Inspiration In Paris
App Allows Eurostar Bookings To Paris And Beyond
Banana Republic Opens In Paris
Beckham Linked With Move To Paris
Chanel Offers Paris Blue Skies Show
Changes Afoot At Paris Airport
Driverless Trains For First Paris Metro
Europeans Flock To Paris Sights
Eurostar Sees Paris Bookings Surge