It has been reported that the move is worth 62m pounds, rising to 89m pounds, with the Blues warding off interest from Arsenal and Sevilla in the 22-year-old winger.
The Ukraine international has enjoyed an impressive rise over the past 18 months after two loan spells away from Shakhtar, breaking into the first team, earning his first cap and scoring in the UEFA Champions League.
Mudryk said the move to Chelsea, who are under pressure after a poor run under Graham Potter which has seen them drop to 10th, was exciting one for him.
“I’m so happy to sign for Chelsea,” Mudryk said.
“This is a huge club, in a fantastic league and it is a very attractive project for me at this stage of my career.
“I’m excited to meet my new team-mates and Im looking forward to working and learning under Graham Potter and his staff.”
Blues owner Todd Boehly said Mudryk was a great addition who could add depth to their attacking options.
“We are delighted to welcome Mykhaylo to Chelsea,” he said.
“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.”