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. Chelsea refused to comment.
However the lack of a top four finish and criticism over Chelsea's stodgy football did for the former Italy coach.
"I would like to thank all of my friends at Chelsea Football Club for their hard work and support over the past two seasons which enabled us to win the Premier League and FA Cup together", Conte said in the LMA statement.
However with Sarri still under contract with Napoli, and Chelsea owner Roman Abramovich reluctant to spend in light of his visa issues, all parties had been left in limbo until Conte was finally relieved of his duties on Friday.More news: United States oil inventories increase in week ending July 13
Uncertainty shrouded Conte's position all last season and it had looked like he would depart in February, after successive losses by a three-goal margin to Bournemouth and Watford.
He had done little to hide his dissent over Chelsea's transfer business in the summer of 2017 and winter of 2017-18, making thinly-veiled criticisms of "the club".
City had agreed a £44m deal a fortnight ago for the eight-times capped player according to reports, but apparently withdrew interest when the price rose.
With two trophies, Conte's spell as boss will likely be considered a success.More news: Collin Sexton is Taking Summer League Way too Seriously
Chelsea finished way behind champion Manchester City and failed to qualify for the Champions League.
Chelsea have also indefinitely postponed plans to rebuild Stamford Bridge in a scheme which would cost more than £1billion.
Blues fans are hoping that the sticky situation is sorted out without further delay as the club play Australian side Perth Glory on July 23 for their first pre-season friendly.
And the Blues could have a new boss and a new midfielder by then.More news: Tesla chief Elon Musk's latest outburst raises doubts on leadership, rattles investors
Jorginho has also made the move from Naples, with the midfielder quickly becoming the first signing of the Sarri era at Stanford Bridge.
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