Conte led Chelsea to the Premier League title in his first season in England in 2016-17 and followed up that achievement with the FA Cup triumph this year, but his relationship with the board became damaged beyond fix, highlighted by his repeated public and private complaints about transfer policy.
The 48-year-old Italian, who returned to pre-season training this week, had one year remaining on his contract.
Ex-Napoli manager Maurizio Sarri is expected to succeed his compatriot at Stamford Bridge.
Antonio Conte was sacked by Chelsea for his alienation of several players and a complete breakdown in communication with the club's board, Sky sources have claimed.
"I wish you every success in the future", he wrote.More news: FIFA Investigation Underway as England Fans Accused of 'Potentially Discriminatory' Chants
Former banker Sarri, 59, will be Chelsea's ninth full-time manager since Roman Abramovich bought the club in 2003.
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.
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.
"Thank you boss", Terry wrote on Twitter. "Great man, Great manager".
Nearly every top-class manager, available and unavailable, has been linked with Conte's job but in the past month or so, Maurizio Sarri has become the hot favourite.More news: Reds set to sign Xherdan Shaqiri by this weekend
Former Spain manager Julen Lopetegui was appointed instead.
After winning the title in his first season, where did it all go wrong for Antonio Conte?
Napoli midfielder Jorginho has reportedly arrived in London to undergo his medical with Chelsea ahead of joining the club.
They reportedly include Brazil-born Italy worldwide midfielder Jorginho from Napoli, CSKA Moscow's Russian playmaker Aleksandr Golovin and Italian defender Daniele Rugani from Juventus, the side that edged Napoli in the Serie A title race.More news: Prince Louis christened while beaming royal family look on
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