Sarri has always been tipped to take over from Conte, however Chelsea dragged out the sacking of his fellow Italian, whose departure was only confirmed today, after two years at the club.
Chelsea have completed the signing of Jorginho, beating Manchester City to the signature of the former Napoli midfielder.
The manager arrives from Napoli with a burgeoning reputation for his brand of football, termed "Sarri-ball".
Conte, meanwhile, leaves after a turbulent 14 months since securing the Premier League title in his first season. "It is an exciting new period in my career".
Conte had been heavily linked with a summer exit from Stamford Bridge after publicly criticising the club's transfer policy, with an FA Cup victory not enough to keep him in the job.
With his appointment now confirmed, the 59-year-old Italian said he was looking forward to the challenge of competing for the Premier League crown after Chelsea slipped to fifth last season - having won the title the year before.
"We are delighted Jorginho has chosen to join Chelsea", club director Marina Granovskaia said in the statement.
Talks had reached an impasse, however, and it soon became clear to De Laurentiis that he would only receive the desired €8 million (£7m/$9m) pay-off for Sarri from Chelsea if it also included in a deal for Jorginho, whom Sarri wanted to bring to Stamford Bridge.
'I look forward to starting work and meeting the players on Monday ahead of travelling to Australia, where I will be able to get to know the squad and begin our match action.
Conte led a team from finishing 10th in the Premier League in the 2015-16 season to becoming champions once again in his first campaign in England.
With little over three weeks left in the transfer window and four until the first Premier League match of the 2018-19, Sarri can not count on time as an ally.
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