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Froome, who was also champion in 2013 and last year, finished ahead of Frenchman Romain Bardet in second and Nairo Quintana of Colombia in third.
For Greipel, who pipped world champion Peter Sagan on the line with Alexander Kristoff third, it was a second successive victory on the final stage and 11th stage win in total.
Froome crossed the line, as he has done before, arm-in-arm with his Sky team-mates stretched out across the road, clad in a special kit in which their usual blue stripe was replaced by a yellow one.
Such was the ease of this, Froome’s most dominant victory yet, that he could even afford to trundle home, losing time to his nearest challengers, safe in the knowledge he had started the day with more than four minutes to play with.
In a typically frantic sprint finish, Greipel timed his charge to perfection.
He took Kristoff’s wheel and darted out at the right time to save his Tour.
Having won four stages last year, he had yet to taste victory this time until Sunday as Mark Cavendish, who quit the race to focus on the Olympics earlier this week, dominated the sprints, winning four stages.
Sagan, typically finished fastest but he left his push a fraction too late and failed to add to his three stage wins this year — his best return at the Tour.
Yet he still won the sprinters’ green points jersey, for the fifth year in a row, at a canter.