Harzand will be aimed at the Prix de l’Arc de Triomphe after joining an elite band of horses to complete the English-Irish Derby double.
The Aga Khan-owned colt gave dual Melbourne Cup-winning trainer his first English Derby and added the Irish equivalent on Saturday (Sunday AEST) on his home track, the Curragh.
Harzand had to show all the qualities of a top-class thoroughbred as Idaho, third at Epsom, refused to go down without a fight.
The leading pair pulled clear in the final quarter-mile (400m), with Harzand, the 4-6 favourite, asserting his authority to win by half a length in the hands of Pat Smullen.
Harzand is the fifth horse to win both English and Irish Classics for the Aga Khan after Shergar (1981), Shahrastani (1986), Kahyasi (1989) and Sinndar (2000).
“I knew Aidan would have his horse better than at Epsom so I knew our horse had to be better than at Epsom to win again,” Weld said.
“He ran a magnificent race. He showed the speed that he has today. People were saying he didn’t have speed, well you saw it today.
“Idaho is a high-class horse, he’s always been that and he was at his best today. It was a great day, a great ride – a special day. It was a proper horse race.
“He’ll have a good break now and we’ll train him for the Arc.”
Harzand remained unchanged with RaceBets at 6-1 second favourite behind Postponed (5-1) for the Arc, which will be run this year at Chantilly on October 2.
Coral cut Harzand to 5-1 from 7-1 for the King George VI And Queen Elizabeth Stakes at Ascot on July 23, for which Postponed is the even-money favourite.