The 48-year-old Italian, who returned to pre-season training this week, had one year remaining on his contract.
Conte won the Premier League in his first season and the FA Cup in May, but the team finished fifth in the league last season, missing out on Champions League qualification.
Ex-Napoli manager Maurizio Sarri is expected to succeed his compatriot at Stamford Bridge.
Should Sarri be appointed, he would be Chelsea's ninth full-time manager since Roman Abramovich bought the club in 2003.
During three years with Napoli, Sarri did not win a major honour but guided the club to second, third and second again - behind Juventus in 2017-18. The former Empoli manager was named Serie A Coach of the Year in 2016-17.
Chelsea announced on Friday that Conte had "parted company" with the club. A 61-word statement ended: "We wish Antonio every success in his future career."
For the sixth time in eight seasons the Premier League's title-winning manager has left his job by the following summer - if not earlier.
Conte has a clause in his contract that guarantees him a pay-off, thought to be £9m, for the final year.
The club's Premier League opener is away at Huddersfield on 11 August.
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