Froome held off lates attacks from rival Tom Dumoulin to secure the lead at the end penultimate day – and wrapped it up by coming home on the final procession stage.
The Team Sky rider now takes his place in this record books as one of the greatest cyclists in history.
Froome, 33, adds the Giro to his Tour de France and Vuelta a Espana titles – only the seventh person in history to win all three Grand Tours races.
The four-time Tour de France champion took a 40-second lead over Dumoulin into Sunday's ceremonial finish in Rome.
In winning his third consecutive Grand Tours, Froome will match the achievements of cycling greats Eddy Merckx and Bernard Hinault.
Dumoulin attacked Froome multiple continually on the finishing climb of the 133-mile stage from Susa to Cervinia on Saturday.
But despite making five attempts in total, he was unable to break the will of British star Froome.
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After Dumoulin's fifth attack, Froome responded with an acceleration of his own and dropped Dumoulin briefly.
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