Chelsea have paid Shakhtar an initial £62m for Mudryk's services.
The 22-year-old had been courted by Arsenal over the last two transfer windows and the Emirates Stadium looked likely to be his next destination but Chelsea swooped in with late interest to get the deal over the line.
Mudryk is Chelsea's fifth signing in the January transfer window after Benoit Badiashile, David Datro Fofana, Andrey Santos and Joao Felix.
He has made 18 appearances in all competitions for Shakhtar this season, scoring, 10 goals and providing nine assists.
Mudryk was in attendance as Chelsea defeated Crystal Palace 1-0 at Stamford Bridge on Sunday.
"I'm so happy to sign for Chelsea," Mudryk told his new club's official website.
"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 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.'
