Blues director Joe Shields, who knows the youngster from his time at Man City, is reportedly the pivotal figure behind the deal.
The Palmer signing falls in line with Chelsea’s new strategy of signing youngsters.
The 21-year-old will compete with agemate Noni Madueke on the right flank while deputising in the number ten role.
Palmer said (via Chelsea’s official website): “I’m excited to get started, and it feels great to sign.
“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.”
Co-sporting directors Laurence Stewart and Paul Winstanley added: “Cole arrives with experience of winning the Premier League and Champions League.
“He adds further quality and versatility to our attacking unit.”
They praised his ability and highlighted that he has delivered in challenging environments, including at the Under-21 European Championship.
They believe he is ready for this next step and are glad he will make that move at Stamford Bridge.
Palmer’s will allay some fears for Chelsea manager Mauricio Pochettino, who has seen his squad depleted by injuries.
Pochettino has been without star signing Christopher Nkunku, striker Armando Broja and Ukrainian speedster Mykhailo Mudryk.
The arrival of Palmer will give Pochettino more offensive options for their clash with Nottingham Forest at Stamford Bridge tomorrow.
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