Financial details of the transfer were not revealed, but British media reported Chelsea hijacked Arsenal's move for the forward and agreed to pay £88.5 million, of which £26.5 million are in add-ons.
"This is a huge club, in a fantastic league and it is a very attractive project for me at this stage of my career," Mudryk said in a statement.
"I'm so happy to sign for Chelsea," Mudryk said.
"I'm excited to meet my new team-mates and I'm looking forward to working and learning under Graham Potter and his staff."
Todd Boehly, Chelsea chairman, and Behdad Eghbali, co-controlling owner, said: "We are delighted to welcome Mykhailo to Chelsea.
"He's a hugely exciting talent who we believe will be a terrific addition to our squad both now and in the years to come. He will add further depth to our attack and we know he'll get a very warm welcome to London."