The 25-year-old, who was poised to join Tottenham until Chelsea intervened last week, has been granted a work permit and has signed a five-year contract and will wear the number 22 shirt.
"I'm very happy to be here," Willian told the club's website. "It's been a dream of mine to come and play here.
"Chelsea are one of the best clubs in the world, and now I'm going to play for one of the best managers in the world, so I'm very happy and looking forward to it."
Willian had initially held talks with Liverpool over a move to the Premier League after Anzhi's owner, Suleyman Kerimov, decided to slash the club's wage bill.
However, he then looked to have chosen Spurs over a move to Merseyside and flew into London for talks and a medical.
But it then emerged late last week that Chelsea had hijacked the deal and that Willian was bound for Stamford Bridge - and not White Hart Lane.