The Ukraine international has signed an eight-and-a-half-year deal, with the Blues paying Shakhtar a reported £62million - possibly rising to £88m.
The 22-year-old was in attendance for Chelsea's game against Crystal Palace at Stamford Bridge on Sunday.
"I'm so happy to sign for Chelsea," Mudryk told the club's 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."
Mudryk had looked poised to sign for London rivals Arsenal before a last-minute intervention from recruitment head Paul Winstanley and co-owner Behdad Eghbali on Saturday, with the pair flying to Turkey to negotiate the deal.