In a statement, Shakhtar said they "will receive 70 million euros for the player and another 30 million euros is envisaged as a bonus payment."
Mudryk, who was named Shakhtar's player of the year for a second year in a row, caught the eye with his performances in the Champions League group stage where he scored three goals and grabbed two assists.
He is the second Ukrainian player Chelsea have ever signed after former striker Andriy Shevchenko joined the Blues from AC Milan in 2006.
"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 excited to meet my new teammates and I'm looking forward to working and learning under Graham Potter and his staff."
Mudryk will reinforce Chelsea's attack after Graham Potter lost forwards Christian Pulisic and Raheem Sterling to injury.
"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," Chelsea chairman Todd Boehly and co-controlling owner Behdad Eghbali said in a joint statement.
"He will add further depth to our attack and we know he'll get a very warm welcome to London."
Arsenal had reportedly been in talks to sign Mudryk as the Premier League leaders sought cover in attack following Brazilian striker Gabriel Jesus' long-term absence due to knee surgery.
But as they negotiated the price and structure of payments, Chelsea swooped in with Shakhtar saying on Saturday that their president Rinat Akhmetov was close to agreeing Mudryk's transfer to Stamford Bridge.
Chelsea, who play Crystal Palace on Sunday, are 10th in the standings, 10 points off the top four.
Joao Felix's red card on debut has also thrown a spanner in the works ahead of next Saturday's league trip to Liverpool, where Mudryk could make his debut.
