The 48-year-old Italian had been seen as vulnerable despite winning the FA Cup last term having fallen out with both the board and senior players.
However, his second season in charge ended with a limp title defence as his side finished fifth in the Premier League, crucially missing out on Champions League qualification.
Chelsea players took to training on Friday morning for the first time without manager Antonio Conte, after the Italian was officially axed from his post at the helm of Stamford Bridge.
In any event, the working relationship between Conte and Chelsea is over - as soon as that is made public by the club, the appointment of Sarri, with Blues legend Gianfranco Zola as part of the backroom team, will nearly certainly follow shortly after.
Before joining Chelsea, Conte had only coached in his native Italy, leading Juventus to three consecutive Serie A titles from 2012-14 before taking over the national team at Euro 2016. "I wish you every success in the future".
The Italian's main gripe for the past year was Chelsea's failure to land the signings he really wanted for its Premier League title defense.
"If Chelsea are paying him even more, I can understand that too".
Sarri will become the 12th manager to take over the reins at Chelsea since Roman Abramovich bought the London club in 2003.
Former Spain manager Julen Lopetegui was appointed instead.
Two trophies in two seasons but the writing was on the wall.
Jorginho is expected to join Sarri from Napoli but star man Eden Hazard continues to be linked with a move away from west London.
Sarri's future has been up in the air since Napoli hired Carlo Ancelotti as its new coach in May.