Froome was second in the eighth and final stage behind winner Alessandro De Marchi of Italy. It was enough to extend his overall lead and make him the third straight British winner of the race. Bradley Wiggins won last year and in 2011.
''It's been a dream scenario,'' Froome said. ''To come away with the victory plus one of my best friends and teammate Richie Porte in second place overall, I couldn't ask for more.''
Wiggins, his Sky Procycling teammate, won the Tour last year, with Froome finishing second. But with Wiggins pulling out of the showcase race, Froome is the clear favorite. The Tour starts June 29.
''Of course, it's a very positive test for the Tour de France. I know that I'll do everything I can to win it as well,'' Froome said. ''We've got some good reasons to be confident with such a great team.''
Overall, Froome was 58 seconds ahead of Porte, with Spaniard Daniel Moreno 2:12 back in third.
''Tonight I'll be able to have a drink with my teammates to celebrate this great win,'' Froome said. ''In the coming days, we'll go and recognize some mountain stages of the Tour.''
On Sunday, with 3.1 miles left in the 96.4-mile mountainous trek from Sisteron to Risoul, Belgium's Tim Wellens led De Marchi by about 30 seconds but was midway up the final climb.
''This victory rewards me for all the unsuccessful breakaways I've conducted since I turned professional,'' De Marchi said. ''It was the dream of my life to achieve something like this and I'm delighted it happened at such a big race. I've tried so many times.''
Froome wanted to give Porte the win and tried to help him catch De Marchi, but his teammate could not stay with Froome's attack.
Australian rider Michael Rogers was third overnight but dropped to sixth place overall.