Sarri led Napoli to two second-place finishes in his three seasons in charge of the Serie A side and pushed Juventus all the way for the Scudetto last term.
The Naples native was replaced by Carlo Ancelotti as Napoli coach last month but remained at the club as a compensation settlement was agreed with the Partenopei.
"I am very happy to be coming to Chelsea and the Premier League," Sarri told the official club website. "It is an exciting new period in my career.
"I look forward to starting work and meeting the players on Monday ahead of travelling to Australia, where I will be able to get to know the squad and begin our match action.
"I hope we can provide some entertaining football for our fans, and that we will be competing for trophies at the end of the season, which is what this club deserves."
Sarri is the 13th managerial appointment by Blues owner Roman Abramovich since his takeover of the club in 2003.