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By Gilles Le Roc'h
Team Sky's Froome, second overall in last year's Tour behind team mate and compatriot Bradley Wiggins, won the fifth stage ahead of double Tour champion Alberto Contador, who took second place overall.
Saturday's sixth and final stage was won by French champion Nacer Bouhanni as Froome secured his first major stage race victory.
Australian Cadel Evans took third place overall ahead of Spain's Joaquim Rodriguez, winner of stage four.
Froome's win was reminiscent of Wiggins's Paris-Nice victory in 2012, when the 32-year-old rider also claimed the Tour de Romandie, the Criterium du Dauphine and the Tour.
The Kenya-born Froome went toe-to-toe with Contador, Rodriguez, Cadel Evans and Italian Vincenzo Nibali on the climbs as he snatched the leader's red jersey after stage four.
Wiggins, who started his season in Oman in a supporting role, was never in contention. (Writing by Julien Pretot; Editing by Pritha Sarkar)