Wiggins, who virtually sealed victory with his second time-trial win of the three-week epic on Saturday, finished the 3,479km race with a 3min 21sec lead over British team-mate Chris Froome after the 20th and last stage to Paris.
It was Isle of Man sprinter Cavendish's fourth consecutive win on the Champs-Elysees, taking his tally of stage wins this year to three and to 23 overall.
"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 Scot Robert Millar's 1984 best British finish of fourth overall, in 2009, Wiggins finally achieved his childhood dream of winning the world's most prestigious bike race.
Italian Vincenzo Nibali of the Liquigas team finished third overall at 6:19.
"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.
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.
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 Briton 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 Froome.
Sagan, meanwhile, came close to claiming his fourth stage win when he came fighting back at the finish to cross the line just short of Cavendish.
But the Slovakian was more than happy with his debut.
"I came here to win a stage, so to come away with three plus the green jersey is just unbelivable," 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."