Chelsea had announced on Monday that they had agreed terms both with Anzhi and the 25-year-old himself to bring him to Stamford Bridge for a reported £32.5 million.
The deal was confirmed on Wednesday after the player was granted a work permit, with the player signing a five-year contract at Stamford Bridge..
'I'm very happy to be here, it's been a dream of mine to come and play here," Willian said.
"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."
The transfer has drawn some criticism, with Chelsea stepping in after Willian had undergone a medical with Tottenham Hotspur last week - much to the chagrin of Spurs chiefs.
But Tottenham's own interest only came after the player had reportedly agreed to join Liverpool the week before.
Willian, who can play as an attacking midfielder or winger, joined Anzhi from Ukraine's Shakhtar Donetsk in January, where he scored 20 goals in 140 league appearances.
Anzhi owner Suleiman Kerimov has reportedly put his entire first team up for sale, having sacked coach Rene Meulensteen.
Willian joins Germany forward Andre Schurrle, Dutch midfielder Marco van Ginkel and Australia goalkeeper Mark Schwarzer as recent arrivals at Stamford Bridge.
He is the latest addition to a long list of attacking midfielders at the club which includes Juan Mata, Frank Lampard, Oscar, Eden Hazard, Victor Moses, Kevin De Bruyne and Schurrle.