Tom Dumoulin (Sunweb) finished second at 46 seconds with Miguel Angel Lopez (Astana) third at almost five minutes after the largely ceremonial 115km 10-lap final stage held in Rome which took the peloton past monuments like the Colosseum, Spanish Steps, Circus Maximus and Baths of Caracalla.
Riding in the gruelling race for the first time since 2010, Froome added the one Grand Tour missing from his collection.
“It's great to soak up the atmosphere here in Rome," Froome said. "I was surely not disappointed by the crowd and the monuments. I need a bit of time to reflect but this race has been incredible.
The 33-year-old joined an exclusive club that includes cycling greats Eddy Merckx and Bernard Hinault as one of only three riders to capture all three Grands Tours in succession.
"For any cyclist, it's a dream to have all three Grand Tour leader's jerseys," Froome said. "I'm still pinching myself. I can't believe I'm here in the Maglia Rosa.”
Froome, who crossed the finish line on Sunday with his hands on the shoulders of Sky teammates, won the Tour de France and Vuelta a España last year and his success at the Giro was built on a remarkable performance in Friday's 19th stage, which put him in full control to win the Maglia Rosa.
Froome turned the race on its head in that stage and saw off several late attacks by Dumoulin to come into contention after being off the pace in the opening week.
The Team Sky rider won while under investigation over an adverse doping test result following a urine sample at last year's Vuelta that showed excessive use of an asthma inhaler. The four-time Tour de France winner has denied any wrongdoing.
Sam Bennett (BORA-hansgrohe) won the stage, which was neutralised after the first three laps, ahead of Elia Viviani (Quick-Step Floors) and Jean-Pierre Drucker (BMC).
With riders concerned about treacherous road conditions due to the uneven cobblestones, the stage was neutralised after three laps, meaning the final overall times were recorded after one-third of the way through the stage.
“I don't know how I managed to beat Elia Viviani," Bennett said. "I suffered so much over the past few days in the mountains. But my team did a fantastic job to bring the last breakaway back today.
"It's fantastic to have won three stages in the Giro but I'll have to get up tomorrow and focus on further goals, possibly the Irish championship as I'd love to show the national colours on the world stage.”