Napoli’s president revealed Sarri was close to finalising a deal to take over at Chelsea on Wednesday, two days before Antonio Conte’s sacking was confirmed by the Premier League club.
Former Chelsea forward Gianfranco Zola will be appointed as his assistant, according to Sky in Italy.
Sarri said: “I am very happy to be coming to Chelsea and the Premier League. 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.”
A series of misdemeanours – the most recent a 20,000 euros fine and two-game ban in January for alleged homophobic abuse of Roberto Mancini – looked to have steered the west London club away from appointing the 60-year-old.
Sarri was replaced by Carlo Ancelotti as Napoli manager last month but remained at the club as a compensation settlement between the 51-year-old and the Serie A club was agreed.
According to Sky sources, Napoli midfielder Jorginho also arrived in London on Friday ahead of a potential £57m move to Chelsea.
Sky Sports News understand Chelsea and Napoli have agreed a deal which features an initial £50m fee with £7m in bonuses.
Man City were also understood to be keen to sign the defensive midfielder.