Revived by Conte after finishing 10th last term in defence of the title won in 2014-15, the Blues clinched the trophy with a 1-0 win at West Brom on Friday night.
And they will seek to complete a double in Conte’s first season by winning the FA Cup final against Arsenal on May 27.
“This is a dream that is coming true,” said Conte, who has won four successive domestic championships after three with Juventus.
“I think that now it’s very important to enjoy this moment and to celebrate this win. To win in England is not easy.
“Don’t forget last season was a bad season for the club, for the players, for the fans.
“Only one year later to celebrate this win in a league where there are for me big, big teams with great players, great managers, it’s great.
“It’s important to celebrate now. We have also another target to try to reach. We worked very hard to reach the final in the FA Cup.
“Then it’s important to prepare in the right way next season.”