The west London club announced the sacking of Conte, 48, with a brief statement on its official website on Friday, despite the Italian having led his side to FA Cup glory at Wembley in May.
Sarri was widely expected to be the next man in the Stamford Bridge dugout after a successful spell in Naples, where his exciting brand of attacking football helped secure successive Champions League qualifications.
He was succeeded in May by Carlo Ancelotti – himself a former Chelsea manager.
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.
“I am very happy to be coming to Chelsea and the Premier League – it is an exciting new period in my career,” he said.
“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.
“I hope we can provide some entertaining football for our fans, and that we will be competing for trophies at the end of the season, which is what this club deserves.”
Club director Marina Granovskaia added: “We are delighted to welcome Maurizio and are looking forward to him bringing his football philosophy to Chelsea.
“Maurizio’s Napoli side played some of the most exciting football in Europe, impressing with their attacking approach and dynamism, and his coaching methods significantly improved the players at his disposal.
“He has plenty of experience in Serie A and the Champions League and we know he is relishing the chance to work in the Premier League.”
Sarri is the 13th permanent boss at Chelsea since Russian billionaire Roman Abramovich bought the club in June 2003 and the sixth Italian to get the job.
His predecessor – whose departure was rumoured throughout the last campaign as he appeared to be unhappy with the club’s transfer decisions – lasted just two seasons.
Chelsea will contest the Community Shield against Manchester City next month, before beginning their Premier League campaign at Huddersfield, followed by a derby against Arsenal – who also have a new manager in Unai Emery.