Wiggins, who clocked one hour, four minutes and 13 seconds, at 50kph, left his nearest rival, teammate Chris Froome, 1:16 behind, quashing suggestions his compatriot was the stronger rider on this Tour.
Froome should be second on the podium on the Champs-Elysees, 3:21 behind his Team Sky leader as the final stage is usually a leisurely ride to the finish line for all but the sprinters.
Italian climber Vincenzo Nibali rode a solid time trial, finishing 16th to retain his third place overall, 6:19 behind Wiggins.
Wiggins, a three-time track cycling Olympic champion, punched the air in joy as he crossed the line as if he had a point to make in this long solitary effort.
"I really wanted to finish with a bang. This is the Tour. It doesn't get much bigger than this," he said.
After completing his ride, Wiggins rushed to his team bus to embrace Froome and Australia's Mick Rogers, two of the Team Sky riders who have helped him in the race.
"We rode this Tour as a unit. I'm very proud of our team work," said Team Sky principal Dave Brailsford.
"Our ambition was to win this race within five years and we did it. It might be a surprise to everybody else but it's not a surprise for us," he added.
Froome readily accepted defeat.
"We saw today he was the strongest. I'm very happy. The goal was to win the Tour with Bradley. We made it. To be second is only a bonus," he said.
There was never any doubt about Wiggins's victory on the flat, windswept course from Bonneval as the Briton, sporting a helmet with a Mod roundel, clocked the fastest time at every intermediate check point.
"I rode the course in March with Sean Yates and I was trying to envisage then what it would be like riding for the yellow jersey to win the Tour. Here we are end of July, job done almost," Wiggins said.
"It was not a lap of honour, but to finish the Tour on what I do best, which is time trialling, is just beautiful," he added.
Suddenly emotional, Wiggins recalled his past disappointments -- a 23rd-place finish in 2010 and the crash which left him with a broken collarbone a year ago.
"I then watched Cadel (Evans) win the Tour in Grenoble. I can imagine how he feels now," Wiggins added.
Australian Evans finished 52nd on the stage, 5:54 off the pace, and suffered the humiliation of being overtaken by young team mate Tejay Van Garderen, who started three minutes behind him.
He will have to settle for seventh overall while 23-year-old American Van Garderen will reach Paris as the best young rider in this Tour in fifth place.
"Cadel had a bit of a problem with sickness on this Tour. I still think he has another Tour win in him. If he comes back next year to win it, I'll be around to help him," said Van Garderen.
For Wiggins, there will be no time for celebration just yet as his next goal is the Olympic time trial gold medal in London on August 1.
""Next goal is the Olympics. It's always been the plan. The Olympics time trial is the next one, so no wine yet," he said.
