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.
TOP 10 FINAL ! #TDF2016 pic.twitter.com/Mwf2MlKdO6
— Le Tour de France (@LeTour) July 24, 2016
FROOME + LE TOUR = πππππ@ChrisFroome remporte son 3Γ¨me @LeTour !@ChrisFroome wins his 3rd @LeTour !#TDF2016https://t.co/7ER3bdBYgK
— Le Tour de France (@LeTour) July 24, 2016