The 25-year-old had won the penultimate stage on Saturday, to move within 0.86 seconds of Hindley going into the 15.7km time trial.
The Ineos-Grenadiers rider beat the Australian to win the race by 39 seconds, becoming only the second Brit to win the Giro, after Chris Froome’s 2018 triumph.
Dutchman Wilco Kelderman, Hindley’s team mate at Sunweb, took third place overall, 1:29 off the pace, with the individual time trial between Cernusco sul Naviglio and Milan won by Italian Filippo Ganna.
The race had been rescheduled from May
9-31 amid the COVID-19 crisis.
Geoghegan Hart’s victory came on the back of a largely disappointing Tour de France from Ineos-Grenadiers after defending champion Egan Bernal pulled out injured in the final week having previously dropped out of contention.
The Giro started in horrific fashion for the British outfit as leader Geraint Thomas pulled out after a crash early in the race, only for the team to win seven stages with Geoghegan Hart moving up the ranks until he snatched the overall lead on the last stage.
Additional reporting by Reuters.