The British cyclist finished third on Stage 20 to Annency-Semnoz, behind Colombian Nairo Quintana and Spaniard Joaquim Rodriguez.
Froome defended his significant lead over his main rivals on the final day in the mountains, and will wear the yellow jersey from Versailles into Paris on Sunday.
Spain’s Alberto Contador, who was second overall going into Stage 20, fell off the pace on the final climb and dropped to fourth overall at seven minutes and 10 seconds behind Froome.
Contador’s inability to follow the pace in the final parts of the climb left Froome, Quintana and Joaquim Rodriguez to forge on ahead and fight it out for the stage victory.
Froome tested his rivals with a short burst of acceleration but the Team Sky leader could not respond when Quintana pulled ahead inside the last two miles.
Quintana went on to cross the finish line alone to claim his maiden stage win on his race debut, moving up to second overall at five minutes and three seconds behind Froome, a day before the final stage in the capital.
Rodriguez came over the line 17 seconds adrift, but the Katusha team leader’s efforts moved him up to third overall at five minutes and 47 seconds behind Froome.
The race ends with Stage 21 on Sunday when Froome is virtually guaranteed to become the second Briton, after teammate Sir Bradley Wiggins last year, to win the world’s biggest bike race.