Pochettino: Rising star Palmer perfect for Chelsea project
Palmer has agreed a seven-year contract with Chelsea, who have a club option of a further 12-month extension, and could pay City an extra £2.5 million in add-on clauses.
City were keen to keep Palmer, but the size of Chelsea's offer eventually persuaded them to cash in on a rising star who was keen for more regular first-team opportunities.
The 21-year-old's arrival takes Chelsea's spending on players to over £1 billion in little over a year since a consortium fronted by LA Dodgers co-owner Todd Boehly took control of the club.
Much of that has been spent on tying down highly-rated prospects to lengthy contracts as Boehly bets on beating the market in the long run.
"I think he's a fit for the project," said Pochettino. "He's a young, talented player. He decided to come because he expects to play maybe more and be important here.
"But that's not the most important thing. The most important is that he sees Chelsea as a project for him, and to improve his game, and to be more involved every single game.
"The quality is there, there is great potential. Now he needs to settle here and prove and show that he's better than his teammates and that he deserves to play. He has to fight for his place."
'Do something special'
Palmer scored in both the Community Shield and UEFA Super Cup last month as Riyad Mahrez's departure from City looked to have opened the door to more first-team minutes under Pep Guardiola.
But the winger said he believed Chelsea would provide him with the platform to develop.
"I'm excited to get started and it feels great to sign," said Palmer, who could make his debut at home to Nottingham Forest on Saturday.
"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 is the 12th player to be signed by Chelsea since the end of last season, with his arrival coming after Pochettino stated he was keen to sign another forward.
A graduate of the City academy, he established himself as a regular in Guardiola's squad last season, making 25 appearances in all competitions as City won the Premier League, Champions League and FA Cup.
He also enjoyed success alongside his new Chelsea team-mates Levi Colwill and Noni Madueke as England won the Under-21 European Championship earlier this year.
"Cole arrives with the experience of winning the Premier League and Champions League and adds further quality and versatility to our attacking unit," Chelsea co-sporting directors Laurence Stewart and Paul Winstanley said.
"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."