"I am absolutely ecstatic to be here at Chelsea", he told the club's website.
"If he creates a team as entertaining to watch as Napoli were under his stewardship then Chelsea's fans are in for a treat", he said on Twitter.
During three years with Napoli, Sarri helped the club to two second-placed finishes in Serie A and won the Coach of the Year award in 2017.
Napoli midfielder Jorginho is poised to reunite with Sarri quickly as the Italian midfielder is already in London to conduct a medical.
His first game in charge will be in the friendly with A-League side Perth Glory at Optus Stadium in Perth on July 23.
And while the dispute between Conte and Chelsea continues to rage on behind the scenes, the Telegraph are now reporting on the ways in which Sarri must now get to grips with his new side and the problems he must deal with over the remainder of the summer.
Jorginho joins Chelsea from Napoli
But Sarri can not concern himself about Abramovich's long-term interest, following the Russian billionaire's visa dispute with the United Kingdom authorities, or the indefinite postponement of plans to rebuild Stamford Bridge.
Having agreed a £50million fee with Napoli just a week beforehand, City and are now reportedly claiming that the Serie A club used heavy-handed tactics to influence proceedings in Chelsea's favour.
Conte thanked his players, staff and the Blues fans, adding: "It was fantastic for me to be able to share my emotions, passion and enthusiasm throughout two unforgettable seasons with these unbelievable Chelsea supporters, who will always stay in my heart".
Conte thanked his players, staff and the Blues fans - and perhaps the omission of the Chelsea board and owner Roman Abramovich was deliberate and notable.
LMA chief executive Richard Bevan anticipates Conte will be sought after following his stint at Chelsea.
'We wish Antonio every success in his future career'.