The 21-year-old has signed a seven-year contract at Stamford Bridge with the option for a further year.
Palmer came through the Manchester City youth system and made over 40 appearances for the first team.
Palmer has had a fruitful year internationally and at club level, helping Manchester City win the FA Cup, Premier League and UEFA Champions League last season as well as the UEFA Super Cup last month and was part of England's U-21 European Championship winning side this summer.
He played in Manchester City's opening Premier League game this season and scored in both the Community Shield against Arsenal and Sevilla in the UEFA Super Cup.
"I'm excited to get started and it feels great to sign," Palmer said.
"I've joined Chelsea because the project here sounds good and because of the platform I will have to try to showcase my talents.
"It is a young and hungry squad and, hopefully, we can do something special."
"Cole arrives with the experience of winning the Premier League and Champions League and adds further quality and versatility to our attacking unit," said Chelsea co-sporting directors Laurence Stewart and Paul Winstanley.
"He has showcased his talent and potential in the most challenging environments and delivered on the international stage for England at the European Under-21 Championships.
"He is undoubtedly ready for this next step and we are delighted it will be with Chelsea."
