The 48-year-old Italian had been seen as vulnerable despite winning the FA Cup last term having fallen out with both the board and senior players.
In Terry's final season at Stamford Bridge, Chelsea sailed to the 2016/17 Premier League title in a convincing fashion in what was a fitting end to the defender's time with his boyhood club.
But he was warned not to follow the title success with "a Mourinho season" in reference to their slump of 2015-16 when they finished 10th, a year after winning the league under the Portuguese.
"We wish Antonio every success in his future career", the statement read.
Chelsea have endured a turbulent summer so far with managerial uncertainty meaning they've yet to make a major signing so Jorginho is expected to become the first new arrival at Stamford Bridge.
Under Sarri's tutelage, Dries Mertens has been transformed into one of the continent's most potent attacking threats, the Belgian scoring a whopping 56 goals in the last two seasons for the free-flowing Partenopei. "Great man, Great manager". Sarri, 59, is expected to replace his compatriot.
Chelsea manager Antonio Conte, pictured with the FA Cup trophy in May, has been sacked after two years in charge.
Sarri is a big fan of the striker, who played under him at Napoli, and Chelsea want to add more firepower to their squad.
He also clashed with senior players such as Diego Costa and David Luiz while others had begun to grow tired of his methods. Attention will then turn towards securing Sarri and Chelsea's other summer targets, believed to include players such as Aleksandr Golovin and Daniele Rugani.