The Englishman left Premier League side Brighton for Stamford Bridge, with Chelsea praising his “progressive football and innovative coaching”.
The 47-year-old has won wide admiration for his work in Brighton, on the south coast of England.
He led the Seagulls to ninth place last season and fourth this season while demanding entertaining and tactical performances from his players.
Potter’s first game as Chelsea manager will be a derby at neighbors Fulham in west London on Saturday.
“I am incredibly proud and excited to represent Chelsea FC, this fantastic football club,” he said.
“I am extremely pleased to be associated with Chelsea’s new group of owners and look forward to meeting and working with this exciting group of players and developing a team and a culture that our incredible fans can be proud of.”
Chelsea chairman Todd Boehly, who knocked out Tuchel on Wednesday after just seven games in the new season, said he was “delighted” to bring Potter to the club.