The Chelsea players have been informed about the decision and were given the afternoon off from pre-season training on Thursday.
Sarri's arrival will mark an end to Antonio Conte's tumultuous two-year spell at the club.
Despite winning the Premier League title in his first season and the FA cup in May, it appears Conte wasn't particularly well liked by some of the Chelsea players due to his naturally defensive, robust style.
He would have frozen out David Luiz, Willian and others, while Chelsea feared that Eden Hazard would not sign a new contract if Conte stayed on and were anxious by his relationship with key players.
However, they finished fifth in the 2017/18 season, missing out on a place in the Champions League and consequently costing Conte is job.More news: Elderly woman mistakenly steals vehicle , drives it for 2 weeks
Last season's FA Cup champions are also interested in signing CSKA Moscow's Aleksandr Golovin and also £35 million rated Juventus defender Daniele Rugani.
Sarri, who split his time between banking and playing football before he took up coaching aged 40, has not won a major honour in three years at Napoli but has guided the club to finishes of second, third and second again.
Maurizio Sarri has already been replaced by Carlo Ancelotti as Napoli boss.
Sarri is believed to have agreed to bring former Chelsea favourite Gianfranco Zola - whose managerial career has stalled after a series of failures - along as one of his backroom staff. His departure has been expected all along but the fans and players alike had been left in a limbo - until now that is.
The Blues had previously been in talks with Napoli over a compensation package and the Serie A giants' president, Aurelio De Laurentiis, said on Wednesday: "Sarri is close to being the new Chelsea manager".
Sarri could be followed by midfielder Jorginho from Napoli, with Chelsea willing to pay £50m, plus £7m in bonuses, for the pair.