The 32-year-old cyclist passed up the chance to celebrate his win in Paris, instead returning to Britain to focus on the London 2012 men's road race and individual time trial.
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"Everything turns to the Olympics and I'll be out on the bike on Monday. I've got an Olympic time trial to try and win," he said.
"It's a little weird to leave Paris without a party because it would be nice to spend time with the team and really enjoy it."
The three-time Olympic track champion will compete in the Olympic road race on July 28 and the time trial on August 1.
Union Flags waved and thunderous cries of "Allez Wiggo!" rang out on Sunday as a joyful Bradley powered down the Champs-Elysees and into the history books as the first Briton to win the Tour de France in the race's 109-year history.
The sportsman looked close to tears after he crossed the finish line, raising his arms in a victory salute.
Tens of thousands of spectators had gathered to watch the defining moment, which took place on a glorious sunny day in Paris.
After hugging his British team mate Chris Froome, who came second overall, he was then congratulated with kisses and hugs by his 30-year-old wife Catherine, and their children Ben, seven, and five-year-old Isabella.
It was the best end possible to 2,173 miles of racing over three grueling weeks.
Accepting the cup, Bradley bowed to the British fans before opera star Lesley Garrett sang God Save The Queen.
"I just want to say thank you to everyone for the support all the way around. It has been a magical couple of weeks for the team and British cycling," he said.
"Sometimes dreams come true and to my mother over there, her son has now won the Tour de France. Have a safe journey home and don't get too drunk tonight."
It was a proud moment for Bradley's 55-year-old mum Linda, who raised him as a single mother on a council estate in Kilburn, North West London.
His father, Australian professional cyclist Gary Wiggins, left when Bradley was two.
The pair were reunited when the sportsman was 19, but drifted apart again before Wiggins senior died in hospital aged 55.
In his autobiography, In Pursuit of Glory, Bradley wrote fondly of his father.
"He may have gone Awol for most of my life but his achievements as a cyclist and almost "legendary" hard-man status on the circuit undoubtedly helped propel me towards a competitive career in the sport. Our shared DNA is at the heart of the story."