By SABC Sport
1st September 2023
According to media reports, the club will pay an initial £40 million for the 21-year-old academy graduate with an additional £2.5 million in possible add-ons.
It is understood a deal was struck on Wednesday for a player City had been keen to keep but were ultimately persuaded to part with by the size of Chelsea's bid.
"I'm excited to get started and it feels great to sign," Palmer told his new club's website.
"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."
It takes spending in the 16 months since the club was acquired by Todd Boehly's Clearlake Capital consortium to over £1 billion, with Palmer the 12th player through the door during the summer transfer window.
Manager Mauricio Pochettino has stated repeatedly in recent weeks that he has been keen to sign another forward player but would only be tempted back into the market for the right profile of player.
Palmer played 14 times in the Premier League last season as Pep Guardiola's side won a third consecutive title, and was an unused substitute during their Champions League final victory over Inter in Istanbul.
He began this season by scoring a spectacular goal at Wembley in the team's 1-1 draw with Arsenal in the Community Shield, a match they went on to lose on penalties.
He was also City's scorer in the Super Cup draw with Sevilla in Athens last month which ended in a victorious penalty shoot-out.