Potter, 47, leaves Brighton to sign a five-year contract at Stamford Bridge after the Seagulls gave Chelsea permission to hold talks with their manager.
Former Tottenham manager Mauricio Pochettino, who is currently without a club, was also considered for a role.
Potter will take charge of his first game as Blues boss on Saturday in the west London derby against Fulham at Craven Cottage.
Potter began building his stellar reputation away from English football with Ostersund, who were playing in the fourth tier of Swedish football when he took over as head coach in 2011.
Within six years he has guided the club to the top flight and to the Europa League where they claimed a famous scalp over Arsenal at the Emirates Stadium in 2018.
After a season in the Championship with Swansea, Potter joined Brighton in 2019 where he has overseen an impressive transformation of the club, completely changing their style of play with his brand of attacking and tactically flexible football winning him plenty of admirers.
Potter has led Brighton to 15th, 16th and ninth places finishes in his three seasons in charge with the Seagulls currently fourth in the Premier League having won four of their opening six matches.
Brighton are expected to collect around £16million in compensation from the deal that takes Potter to west London.
‘I am incredibly proud and excited to represent Chelsea FC, this fantastic football club,’ Potter said.
‘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.
‘I would also like to place my sincere thanks to Brighton & Hove Albion for allowing me this opportunity and in particular Tony Bloom and all the players, staff and supporters for their continued support during my time at the club.’
Todd Boehly, Chelsea chairman, said: ‘We are thrilled to bring Graham to Chelsea. 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.’
Tuchel meanwhile leaves Stamford Bridge after 20 months in charge, having won the Champions League within his first five months at the club.
The German was sacked by Chelsea on Wednesday morning following a dismal defeat to Dinamo Zagreb in their Champions League group stage opener the previous night.
His dismissal comes after losing the confidence of the Chelsea squad and the new ownership led by American businessman Todd Boehly, whose consortium acquired the club in May.
The Blues have endured an underwhelming start to the season despite spending in the excess of £270million on new signings this summer.
While only five points off the top, Chelsea have won just three of their opening six games, suffering defeats to Leeds United and Southampton.
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