The 10-11 shot, second in the Derby at Epsom behind stablemate Golden Horn, scored by five lengths from Storm The Stars, with Giovanni Canaletto third.
Jack Hobbs is the first British-trained winner of the race since Commander In Chief, for Henry Cecil, in 1993.
Storm The Stars (10-1), who was third at Epsom, made the running but Jack Hobbs powered past for victory.
"It was genuine good to firm ground and it's nice to see the form from Epsom working out so solidly," said Newmarket trainer Gosden.
"He travelled really well and William just waited after he came at the head of the straight and I loved the way he finished off his race.
"The second horse has run a blinder and he was third at Epsom."
He said the horse would be rested before contesting the Prix Niel in September and the Prix de l'Arc de Triomphe the following month.
Bookmakers reacted by cutting Jack Hobbs' odds for the Arc to around 7-1 (from 14s) behind 3-1 favourite Treve and 4-1 chance Golden Horn.
Sheikh Mohammed's Godolphin racing  team bought a majority share in the colt after he was runner-up to Golden Horn in the Dante Stakes at York in May.
"I had a lot of belief in him before Epsom and he was even better today. He's a horse that's improving all the time," said Buick.
Favourite Jack Hobbs won the 150th Irish Derby at the Curragh under jockey William Buick for trainer John Gosden.