Willian has completed his £32 million transfer to Chelsea after the Brazilian was granted a work permit.
The 25-year-old arrived in London last week ahead of an expected move to Tottenham, however Chelsea hijacked the deal at the 11th hour to sign their fourth player this summer.
Willian will wear the No.22 shirt at Stamford Bridge and has signed a five-year contract.
"I'm very happy to be here, it's been a dream of mine to come and play here," Willian told the club website.
"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's signing takes Chelsea's summer spending up to £63.46m.
Adept as an attacking midfielder or winger, Willian joins a plethora of forwards available at manager José Mourinho's disposal.
Chelsea supporters will be familiar with the former Corinthians player, who scored twice in Shakhtar Donetsk's unfortunate 3-2 group stages defeat in West London last year.
His arrival will cast further doubt on Juan Mata's future at Chelsea, however.
The Spaniard's father and agent, Juan Mata Senior, was reported to have been in attendance for Arsenal's Champions League victory over Fenerbahçe on Tuesday night at the Emirates Stadium.
Gunners manager Arsène Wenger admitted after the match he was an admirer of Mata, named Chelsea's player of the year in each of his two seasons at the club.