Ex-Napoli manager Maurizio Sarri is expected to succeed his compatriot at Stamford Bridge.
Chelsea football club are allegedly accusing Conte of breaching his contract after confirming the end of his employment on Friday morning.
"We won our sixth league title and eighth FA Cup".
The Italian has taken most of his backroom staff with him with only Paolo Bertelli, Carlo Cudicini and goalkeeping coach, Gianluca Spinelli, considering staying at Chelsea for the coming season.
Like a number of his predecessors, Conte has been dismissed the season after winning a major trophy, pointing to silverware being no guarantee of job security at Stamford Bridge.
Winning the FA Cup against former Chelsea manager Jose Mourinho's Manchester United in May was scant consolation to finishing 30 points behind champions Manchester City in the league.
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Sarri, who comes off the back of a wonderful season with Napoli, had been sacked during the summer but remains under contract with the Serie A runners-up.
Conte's relationship with the Chelsea hierarchy had soured in the final year at the helm of the club regarding transfers.
The former Napoli boss will be joined by Chelsea hero Gianfranco Zola as his assistant.
At times during the Sarri reign, Napoli played an nearly mesmeric style of football which was just about the most attractive in Europe.
That is not Chelsea's usual protocol and it is also believed lawyers are still haggling over how much to pay the former Juventus and Italy manager.
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.