The 28-year-old, who learned to ride on dirt tracks in Kenya, crossed the finish line in Paris arm-in-arm with his Team Sky colleagues after more than 80 hours and 2,000 miles in the saddle.
He finished four minutes and 20 seconds ahead of Colombian Nairo Quintana in second place as the team hung back to cross the line together.
Froome set off for Paris in the leader's yellow jersey for the final stage of the Tour. He had to wait until he reached the Champs-Elysee to be crowned champion, but tradition dictates the leader is not threatened on the final day of Le Tour.
After winning the title, Froome thanked his family, friends and teammates.
He said: "I'd like to dedicate this win to my late mother. Without her encouragement to follow my dreams I would probably be watching this at home on TV."
Speaking after the finishing line, he said: "It brought tears to my eyes just coming over the line with the guys like that.
"This really was an amazing way to finish off a fitting 100th edition of the Tour de France."
Britain's Mark Cavendish failed to make it five in a row on the Champs Elysees after finishing in third place in a sprint finish.
Marcel Kittel won the stage, with Andre Greipel in second.
British Prime Minister David Cameron led the tributes to the cyclist. He tweeted: "A brilliant win by @chrisfroome.
"After two British winners it's only right the Tour de France comes to Yorkshire next year."
Reflecting on his month-long ride across France, Froome added before the final stage: "It's difficult for me to put it into words. It's been an amazing journey for me.
"The race has been a fight every single day."
Team Sky manager Dave Brailsford set about grooming Froome into a winning rider the moment he joined the squad in 2010.
His protege finished second in the 2011 Vuelta a Espana and helped Sir Bradley Wiggins to success on the Tour de France a year later.
"I'd like to come back and keep contending for the Tour for as long as I can and as long as I have the motivation," he said.
Froome claimed the yellow jersey on stage eight - the first of his three stage wins en route to Paris.
He successfully negotiated the penultimate Annency-Semnoz stage, finishing third behind Colombian Nairo Quintana and Spaniard Joaquim Rodriguez but defending his five-minute lead. - Sky News
