"Thank you Mister for another Premier League title and FA Cup", tweeted Fabregas.
Conte, 48, had returned to full pre-season training at the start of the week despite huge uncertainty surrounding his future at the club, but with one year left on his contract the Blues have chose to relieve the Italian tactician from his duties in west London.
The London club says, "We wish Antonio every success in his future career".
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.
Chelsea have confirmed that they have sacked manager Antonio Conte, though they face the prospect of a prolonged legal battle with the former Juventus boss.More news: Stormy Daniels' Ohio Strip Club Charges Dismissed
Conte's lawyers will dispute the claims made by Chelsea and have begun the work of securing his £9m payoff, due for the remaining final year of his three-year contract at Stamford Bridge. "Great man, Great manager".
Conte's future with the Roman Abramovich-owned club has looked uncertain for months, however, with the West Londoners failing to qualify for the coming season's Champions League after finishing fifth last season.
In May, Napoli appointed Carlo Ancelotti to replace Sarri amid speculation that the latter could take the Chelsea job.
His exit could mean that Chelsea's transfer window finally grinds into gear, with Sarri understood to have already instructed the Blues board to chase a number of players, including Jorginho, who is expected to follow him from Napoli for €58 million.
Only the pay was improved, though, with Conte's contract still running for just another two seasons - hardly a show of commitment by either the club or its manager.