But Chelsea player Cesc Fabregas has thanked Conte on social media and wished him "luck for the future".
According to various reports, former Napoli manager Maurizio Sarri will take over from Conte.
The 48-year-old Italian, who returned to pre-season training this week, had one year remaining on his contract.
Sarri led Napoli to a record points total last season as they finished a narrow second in Serie A behind champions Juventus.
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.
Conte leaves with the best win percentage 65.1% of any of Chelsea's managers in the Premier League era.
Chelsea sacked Conte and nearly his entire staff at the club's Cobham training ground after the Italian took a morning session yesterday, with Sarri now on the brink of taking over. "Great man, Great manager".
Carlo Ancelotti replaced Sarri as Napoli coach following the end of the season, with a Chelsea move having been on the cards since Conte's relationship with the club's senior management turned sour in 2017-18.
The main reason for the prolonged saga has been compensation.
The appointment of Sarri could help Chelsea land Napoli's Jorginho. Gianfranco Zola will return to Chelsea on Sarri's staff.
Sarri has also presented a list of players he would like to sign.