Wiggins, who had virtually sealed victory the previous day, finished the three-week, 3,479km epic with a 3min 21sec lead over British team-mate Chris Froome after Sunday's 20th and last stage to Paris.
He also helped Sky team-mate Mark Cavendish to secure an unprecedented fourth consecutive stage win on the Champs Elysees.
"It's been a magical couple of weeks for the team and for British cycling," Wiggins told the massed throngs who had besieged France's famous thoroughfare, many waving British flags.
"Some dreams come true," he added, after securing the famous yellow jersey in the largely ceremonial final leg.
Wiggins, who received huge support from his Sky team-mates during the gruelling rides through the Alps and the Pyrenees, promised to return the favour and help Cavendish secure Olympic gold in London.
"I'm more than happy," said world champion Cavendish as he held his newborn baby at the finish line. "The Champs Elysees is the most beautiful avenue in the world, and I've won here again."
Three years after Wiggins equalled Robert Millar's 1984 best British finish of fourth overall, the Belgian-born Londoner finally achieved his childhood dream of winning the world's most prestigious bike race.
"It's magnificent," said Wiggins. "For us to finish like this as a team, helping Mark to victory and allowing him to defend his record here... it's incredible."
Team Sky achieved the rare feat of a 1-2 on the podium, the first since 1996, when Dane Bjarne Riis finished ahead of his German team-mate at Telekom, Jan Ullrich.
Italian Vincenzo Nibali of the Liquigas team finished third overall, six minutes and 19 seconds behind Wiggins.
It is also the first time compatriots have taken the first two places since France's Laurent Fignon finished ahead of five-time winner Bernard Hinault in the 1984 edition.
British Prime Minister David Cameron led the tributes, calling Wiggins' victory an "immense feat of physical and mental ability".
"I'm like everyone in the country -- absolutely delighted," he told Sky News.
"I think the whole country wants to say well done, brilliant -- the perfect backdrop and start to the Olympics."
Frenchman Thomas Voeckler of Europcar won the polka dot jersey for the race's best climber, with Slovakian Peter Sagan of the Liquigas team easily securing the green jersey for the points competition.
American Tejay Van Garderen made up for BMC team leader Cadel Evans' disastrous title defence by winning the race's white jersey for the best-placed rider aged 25 and under.
Van Garderen was fifth at 11:04 while Evans, who made history for Australia in 2011, eventually finished nearly 16 minutes adrift.
RadioShack's best finisher was Spaniard Haimar Zubeldia, but the American team topped the coveted teams' classification, allowing them a podium appearance.
Dane Chris Anker Sorensen, of Saxo Bank, was also afforded that pleasure when he was awarded the overall "most aggressive" rider prize.
In a campaign that was reminiscent of his childhood hero, Spanish legend Miguel Indurain, Wiggins' two time-trial wins on stages nine and 19 proved decisive.
However the Briton's Sky team, and especially Kenyan-born Froome, were omnipresent in the mountain stages in between.
"He's been incredible throughout the whole Tour," Wiggins, whose mountain pace-setters proved so efficient that few riders were able to sustain their attacks, said of fellow Briton Froome.
Sagan was more than happy with his tour debut despite being pipped by Cavendish on the Champs Elysees.
"I came here to win a stage, so to come away with three plus the green jersey is just unbelievable," said Sagan, who finished with a 141-point margin over German sprinter Andre Greipel.
Voeckler's two stage wins among a total of three for his Europcar team meant French riders won a total of five of the race's 20 stages.
However Britain, thanks exclusively to Team Sky, won six. Cavendish won three to take his tally to 23, Wiggins won both time trials and Froome won the first hilltop finish on stage seven.
"It's been a very successful race for Team Sky, first and second on GC (general classification) and we've won six stages," said Cavendish.
"It's been incredible to be part of."
The British press on Monday agreed.
Popular tabloid The Sun said "a new British hero", comparing Wiggins to cricketer Ian Botham, footballer Bobby Moore and Olympic rowing legend Steve Redgrave.
0 Comments