Sarri, 59, replaces fellow Italian Antonio Conte, who was sacked on Friday after two years at the West London club.
He led Napoli to two second-place finishes in his three seasons in charge of the Serie A side, before exiting this season to pave the way for Carlo Ancelotti in May.
“It is an exciting new period in my career,” said Sarri.
“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, a former banker, is the 13th managerial appointment by Chelsea owner Roman Abramovich since his takeover of the club in 2003, including Jose Mourinho and Guus Hiddink on two occasions.
Sarri’s appointment had been widely expected, with Chelsea agreeing compensation to bring him to Stamford Bridge because he had two years left on his Napoli deal.
His immediate task will be to bring back cohesion to the side after a rather disappointing defence of their title last season.