Wiggins finished safe in the bunch on the final 20th stage to claim the 99th edition of the famous race Sunday. Wiggins helped his Sky team mate and fellow Briton Mark Cavendish to victory in the 120-km ride from Rambouillet.
"What a finish that was something, Mark won the stage after we led him out in the finale. Wonderful, wonderful," Wiggins told reporters.
Asked about making history, Wiggins added: "I've got to start getting used to that now which is strange. It's mission complete."
Next year, pure climbers Alberto Contador and Andy Schleck are expected to return to the race after a doping suspension and injury respectively, according to a Rueters report
American Lance Armstrong, after a bout with metastasized cancer, went on to win the Tour de France each year from 1999 to 2005, and is the only person to win seven times.
"It's incredible," Cavendish told French TV, holding his baby girl Delilah Grace in his arms.
"For me this race is everything, it's what my whole year is built towards every year," he later told reporters, aware that the London Olympic road race takes place next Saturday.
Overall, Wiggins led compatriot Chris Froome by three minutes 21 seconds and Italian Vincenzo Nibali by 6:19.
"Have a safe journey and don't get too drunk," Wiggins told the thousands of fans as he topped the podium.
Australian Cadel Evans began the race as defending champion, and finished seventh overall. The Aussie was beaten by his American BMC team mate Tejay van Garderen who placed fifth overall to take the white jersey for the best Under-25 rider.
Wiggins is also the first rider to win an Olympic track gold medal and the Tour. The Brit snatched the yellow jersey in the seventh stage at the end of the brutal climb to La Planche des Belles Filles and consolidated his overall lead with a gutsy performance in the individual time trial on stage nine before Team Sky rode defensively in the mountains.