Chelsea - who have now broken the £1billion barrier in just three windows under their Todd Boehly-Clearlake ownership - are paying £40million up front for Palmer with another £5m potentially due in add-ons, with the 21-year-old having put pen to paper on a seven-year contract in west London through 2030 that includes the option for a further 12 months beyond that.
He could be in line to play some part in Saturday’s Premier League home fixture against Nottingham Forest, having been handed the No20 shirt by the Blues.
It was most recently given to Brazilian midfielder Andrey Santos, who joined Forest on a season-long loan last week. Juventus loanee Denis Zakaria wore that number last season, while another previous Chelsea No20 is also on his way to Forest in Callum Hudson-Odoi.
"I’m excited to get started and it feels great to sign," Palmer told Chelsea’s official website on Friday. "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.”
Chelsea’s co-sporting directors Laurence Stewart and Paul Winstanley added: "Cole arrives with experience of winning the Premier League and Champions League and adds further quality and versatility to our attacking unit.
"He has showcased his talent and potential in the most challenging environments and delivered on the international stage for England this summer at the European Under-21 Championships. He is undoubtedly ready for this next step and we are delighted it will be with Chelsea."
Palmer will be helped settling in at Chelsea by a number of familiar faces that include former City players Raheem Sterling and Romeo Lavia, plus England U21 team-mates Levi Colwill and Noni Madueke.
“Raz has always looked after me, so I appreciate him,” Palmer said of reuniting with Sterling.
“He was one when I was coming through at Man City who put his arm around me. That was amazing for me, for someone of his pedigree and international experience to do that.
“He saw the potential I had. He saw what I was doing in training. We started talking a bit more. I was asking him questions all the time and from there we have always kept in contact.
“I’ve played with him in games a few times, not loads, and now I’ve developed my game a bit more, hopefully we can do some good stuff together.”