The 59-year-old was confirmed as Antonio Conte's replacement on Saturday morning, having put pen to paper on a three-year contract at Stamford Bridge.
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.
However, Sarri has also fallen foul of accusations regarding his conduct, with Roberto Mancini accusing his fellow Italian of using homophobic language during a Coppa Italia quarter-final between Napoli and Inter Milan in 2016.
The former Partenopei coach also apologised earlier this year for taking exception to a female reporter's question at a post-match press conference and replying: "You're a woman, you're pretty, for those two reasons I won't tell you to piss off."
According to The Telegraph, Sarri has promised his new employers that there will be no repeat of his previous behaviour.
Sarri is the 13th managerial appointment by Blues owner Roman Abramovich since his takeover of the club in 2003.