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The Italian is the sixth man to win all three Grand Tours - the Tour de France, Giro d'Italia and Vuelta a Espana, the media reports say.
His winning margin of seven minutes 37 seconds over Jean-Christophe Peraud in second is the biggest since Jan Ullrich won by more than nine minutes in 1997.
Germany's Marcel Kittel won Sunday's traditional final-stage sprint finish.
The Giant-Shimano rider outsprinted Norway's Alexander Kristoff to win his fourth stage of this year's Tour, with Garmin-Sharp's Lithuanian Ramunas Navardauskas in third.
For Nibali, the 21st and final stage was all about reaching the finish safely because Tour tradition dictates that the leader going into the final stage should not be challenged.
The 29-year-old Astana rider dominated the Tour from the moment he took the race lead on stage two in Sheffield and wore the race leader's yellow jersey for 18 of the race's 21 days.
He is the first Italian winner of the race since Marco Pantani in 1998.