Froome (Team Sky) finished 1min 12sec ahead of the Movistar duo of Nairo Quintana and Alejandro Valverde, who was third at 5min 25sec.
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Last year's winner Vincenzo Nibali (Astana) finished fourth overall, ahead of two-time former winner Alberto Contador (Tinkoff-Saxo).
"This is such a great race, what can I say? I feel a lot of emotion," said Froome after a Tour in which he was forced to endure the ire of some bitter spectators as well as the form of his rivals.
"Of course it was a very, very difficult Tour, both on the bike and off it. I'm so happy to be here in yellow.
"There were a few difficulties, a few extra stresses outside of the race but that's cycling in 2015.
"I'm happy to be in this position to speak for cycling today."
Quintana also praised Froome's resilience.
"He is a great rival, he suffered a lot for his victory and was very strong. He deserves it," the Colombian said.
After the traditional procession into Paris before 10 laps around the Arc de Triomphe, the stage was won by Greipel. The Lotto-Soudal sprinter finished ahead of Bryan Coquard (Europcar) and Alexander Kristoff (Katusha) in an expected sprint finish.
The victory was Greipel's fourth of this year’s Tour. He had already won the second, fifth and 15th stages in sprint finishes.
Race organisers opted to neutralise the general classification competition after the peloton crossed the finish line for the first time which gave Froome the 2015 victory despite needing another 10 laps to complete the race.
The decision was made because of earlier bad wet weather, which affected the women's La Course race held earlier in the day and caused numerous crashes.
The attacks came at less than 50km to race. The obligatory doomed break contained Nelson Oliveira (Lampre-Merida), Florian Vachon (Bretagne-Séché Environnement) and Kenneth van Bilsen (Cofidis).
Hoping to bookend his Tour de France, Australia’s Rohan Dennis (BMC) bridged from the peloton to make it four at the front. But the peloton would not be denied and the quartet was swamped after another well-timed catch with five kilometres to go.
The stage became a leadout train free for all with Lotto-Soudal and Orica-GreenEDGE the dominant teams at the head of the race. The sprint came down to a man on man effort involving Greipel, Coquard, Kristoff, Mark Cavendish (Etixx-QuickStep), John Degenkolb (Giant-Alpecin) and Peter Sagan (Tinkoff-Saxo).
Froome was not only declared the overall winner of the 102nd Tour de France but also winner of the mountains classification. The best placed Australian was Tinkoff-Saxo’s Michael Rogers who finished almost two hours behind Froome.
Sagan won the points classification for the fourth straight time while Quintana was the best young rider for the second time in his career.
Movistar topped the teams classification and Romain Bardet (AG2R) was awarded the most aggressive rider of the 2015 Tour.
