The 59-year-old was replaced at Napoli by former Chelsea boss Carlo Ancelotti in May after guiding the Partenopei to two second-place finishes and one third spot across his three seasons in charge.
Sarri arrives from Napoli after a long-winded negotiation period between the Italian club and Chelsea over the coach's compensation fee.
As he was still in the final year of a three-season contract, Conte is due a £9m payoff which the club will contest.
"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", he told the club's official website.
Club director Marina Granovskaia added: 'We are delighted Jorginho has chosen to join Chelsea.
Maurizio Sarri had to defend himself against accusations of homophobia and sexism while interviewing for the Chelsea job.
In a drastic change of events, the Napoli midfielder, whose transfer to Manchester City was understood to have been all but completed, joins Chelsea now amidst much confusion and guesswork by pundits and the fans.
A key piece of evidence will be the text message Conte is reported to have sent Diego Costa while he was a Chelsea player.
Bundesliga side even built a temporary wall in the away changing room to split the physio area and allow him space to smoke pre kick off and at half and full time.
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.