It is Conte's first campaign in charge of Juve.
"The sensations are something indescribable, fantastic, extraordinary. We are so happy to have achieved a super-extraordinary season," said Conte.
"I thank the players who worked so hard, the fans who put themselves behind us 100 per cent and I also tip my hat to Milan, who provided a huge challenge and are a great club. It's even more satisfying to get the better of a side like that, as it was unexpected.
"Only the slip-up with Lecce caused a little apprehension, but we are Campioni d'Italia with a round to go and unbeaten after 37 rounds. We hope to end the season unbeaten, as that would be truly historic.
"It is my first Scudetto and I am truly very happy. We want to celebrate on the pitch with our fans, but it's tricky with the chaos that is out there."