Graham Potter had been Brighton manager since May 2019
Potter has left fellow Premier League club Brighton to take up the role and has signed a five-year deal with the Blues.
The 47-year-old said he was "incredibly proud and excited to represent Chelsea".
Potter's first game in charge will be an away derby with fellow west London club Fulham on Saturday at 12:30 BST.
His assistant Billy Reid, first-team coaches Bjorn Hamberg and Bruno, goalkeeping coach Ben Roberts and assistant head of recruitment Kyle Macaulay will join him at the Chelsea, who have paid Brighton in excess of £21m in compensation.
"We are thrilled to bring Graham to Chelsea," said the Stamford Bridge club's chairman Todd Boehly.
"He is a proven coach and an innovator in the Premier League who fits our vision for the club.
"Not only is he extremely talented on the pitch, he has skills and capabilities that extend beyond the pitch which will make Chelsea a more successful club.
"He has had a major impact at his previous clubs and we look forward to his positive impact at Chelsea.
"We look forward to supporting him, his coaching team and the squad in realising their full potential in the coming months and years."
Former Ostersunds FK and Swansea City manager Potter led Brighton to a ninth-place finish last season, the club's highest ever top-flight finish.
He has guided them to fourth in the table this season after winning four, drawing one and losing one of their six Premier League games.
Chelsea decided to sack Tuchel, who won three trophies in 20 months at Stamford Bridge, with the Blues sixth in the top flight following a summer in which they spent £255.3m in the summer transfer window.
"I am very excited to partner with Chelsea's new ownership group and look forward to meeting and working with the exciting group of players and to develop a team and culture that our amazing fans can be proud of," said Potter.
He also offered a "sincere thanks" to Brighton, including chairman Tony Bloom, for their support during his spell of just more than three-years at the club.
Brighton Under-21 coach Andrew Crofts has taken over as Brighton's interim head coach, while attacking midfielder Adam Lallana will be part of his coaching set up.
"I am very disappointed that Graham will be leaving us," said Bloom.
"He has done exceptionally well over the past three-and-a-bit seasons, he is an exceptional head coach and an exceptional person. He will be hugely missed at our football club.
"He leaves an excellent legacy for his successor with the club in its highest ever position, and on the back of leading us to our highest finish in the club's history last season.
"I would like to thank Graham, Billy, Bjorn, Bruno, Ben and Kyle for their work here, and wish them all the very best for the future.
"While our attention is now on appointing Graham's successor as head coach our immediate focus, of course, is on Saturday's game at Bournemouth and supporting Andrew Crofts as interim head coach."
A former full-back in the Football League with Stoke, West Brom and York, Potter began his managerial career with Ostersunds FK in 2010, guiding them from the fourth tier of Swedish football to the first, winning the 2017 Swedish Cup and reaching the knockout stages of the Europa League.
He then took charge of Swansea City in June 2018, spending one season with the Championship side before joining Brighton in May 2019 following Chris Hughton's dismissal.
Potter went on to guide the club to 15th, 16th as well as the ninth-place finish in his three full seasons in charge.
-- Courtesy of BBC Sport