Tuchel was sacked on Wednesday after Chelsea's underwhelming start to the season culminated in a 1-0 defeat to Dinamo Zagreb in their UEFA Champions League group stage opener.
The German tactician led Chelsea to Champions League glory, UEFA Super Cup success and victory in the FIFA Club World Cup before his departure.
Potter has signed a five-year contract at Stamford Bridge and will take charge of the side for the first time against Fulham on Saturday.
The 47-year-old was in charge at Brighton and Hove Albion for three seasons, leading them to their highest place finish in the top flight(9th) last season.
"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," owner Todd Boehly said in Chelsea's announcement.
"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."
"I am incredibly proud and excited to represent Chelsea FC, this fantastic football club," said Potter. "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."
