The attacking midfielder has joined in a deal worth up to £42.5million and has signed a seven-year deal that includes an additional one-year option.
Chelsea will pay an initial £40m with the remainder of the package for 21 year-old Palmer made up of add-ons.
The deal takes Chelsea’s spending since Todd Boehly took over the club last year to £1bn.
‘I’m excited to get started and it feels great to sign,’ said Palmer. ‘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 here.’
Palmer has been keen to secure more regular first-team opportunities after seeing his playing time limited at the Etihad and has been told he will be used on the right side of Chelsea’s attack and as a number 10.
The Blues intend to deploy him in a similar role to what Phil Foden is used at City in a bid to get the best out of the Palmer given his evident potential.
City initially valued their academy talent at £50m but Chelsea reached a compromise for Palmer with £40m fee and a further £2.5m due in add-ons accepted by the reigning English champions.
Palmer broke through the City ranks to make his first-team debut three years ago after coming off the bench in a 3-0 Carabao Cup win over Burnley.
Further cup appearances followed before he went on to feature in the Premier League for the first time against Norwich in March last year.
Palmer scored a superb goal in the Community Shield defeat to Arsenal and in City’s UEFA Super Cup final victory over Sevilla.
The youngster follows in the footsteps of Raheem Sterling who called time on his Etihad career in favour of joining Todd Boehly’s revolution at Stamford Bridge.
‘Raz has always looked after me, so I appreciate him,’ Palmer added.
Chelsea’s spending under Todd Boehly
- Moises Caciedo £115m
- Enzo Fernandez £106.7m
- Mykhailo Mudryk £88m
- Wesley Fofana £73m
- Marc Cucurella £62m
- Romeo Lavia £58m
- Christopher Nkunku £53m
- Raheem Sterling £47.5m
- Cole Palmer £42.5m
- Axel Disasi £38m
- Benoit Badiashille £35m
- Kalidou Koulibaly £34m
- Nicolas Jackson £32m
- Noni Madueke £29m
- Malo Gutso £26m
- Robert Sanchez £25m
- Lesley Ugochukwu £23.8m
- Carney Chukwuemeka £20m
- Andrey Santos £18m
- Deivid Washington £17m
- Pierre Emerick-Aubameyang £12m
- Joao Felix £9.7m (loan fee)
- Gabriel Slonina £9m
- David Fofana £8m
- Jimmy-Jay Morgan £3m
- Denis Zakaria £3m (loan fee)