The 60-year-old replaces Massimiliano Allegri at the Allianz Stadium after leading the Blues to Europa League glory in Azerbaijan last month and steering his side to a third-place finish in the Premier League in his one and only season in the English capital.
Chelsea confirmed the move on Sunday via an official statement which read: "The two clubs have reached an agreement for the early termination of Sarri’s contract with Chelsea FC which had two years left to run and is ending at his request."
Chelsea director Marina Granovskaia said: "In talks we had following the Europa League final, Maurizio made it clear how strongly he desired to return to his native country, explaining that his reasons for wanting to return to work in Italy were significant.
"He also believed it important to be nearer his family, and for the well-being of his elderly parents he felt he needed to live closer to them at this point.
"Maurizio leaves Chelsea with thanks from us all for the work he and his assistants did during the season he spent as our head coach, and for winning the Europa League, guiding us to another cup final and a third-place finish in the Premier League.
"We would also like to congratulate him on securing the role as big as any in Serie A and to wish him the best of luck for the future."
Outside of his 12-month stint in west London, Sarri has spent his entire career in Italian football, managing the likes of Perugia, Empoli and Napoli before making the switch to Stamford Bridge in 2018.
In total, he won 39 of his 63 games in charge at Chelsea, losing just 11 times.
Lampard – the club’s all-time leading goalscorer – would become Roman Abramovich’s third appointment in three years, following in the footsteps of Sarri and new Inter boss Antonio Conte.