Team Sky's Froome, the winner of three stages, claimed his maiden yellow jersey with a winning margin of 4min 20sec on second-placed Colombian Nairo Quintana of Movistar.
Race debutant Quintana, who moved up to second place thanks to his maiden stage win at the summit finish of Annecy-Semnoz yesterday, secured the race's white jersey for the best young rider and the best climber's polka dot jersey.
Slovakian Peter Sagan of Cannondale won the points competition's green jersey for the second successive year.
Greipel, the winner of one stage, finished second with Cavendish, a close third.
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It leaves Kittel, with four stage wins, as the top sprinter of this year's race.
Froome began the final stage with a lead of 5:03 on Quintana -- the largest winning margin since disgraced American Lance Armstrong claimed his sixth win in 2004 with a lead of six minutes on German Andreas Kloden.
Froome thus becomes the second successive Briton to win the race after teammate and compatriot Bradley Wiggins, who made history as Britain's first winner in 2012, when Froome finished runner-up.
The 28-year-old Froome, born in Nairobi, won three stages on this year's race -- two on mountaintop finishes and one time trial -- to take his tally to four.