The 48-year-old Italian had a year remaining on his contract, but has left the Blues 55 days after lifting the FA Cup in his final match in charge - and having taken pre-season training earlier this week.
The agreement with Chelsea now looks to have been finalised, with Conte's exit paving the way for Sarri to take over at Stamford Bridge.
Conte's position has been under scrutiny since the middle of last season when relations with the board became strained amid a feeble title defence.
It was clear that the Italian manager would not continue in his role after he fell out with a number of players and openly criticised the club's spending.
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However, while present players may have had issues with Conte, former Chelsea legend John Terry, who left after the league title-winning campaign had nothing but praise for him. "Great man, Great manager".
Former Juventus and Italy boss Conte signed a three-year contract before becoming Chelsea head coach in July 2016.
"I wish you every success in the future".
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.
Ex-Napoli coach Sarri, meanwhile, could be presented as his replacement as early as Friday, with the Blues squad already informed over the change in management.