The transfer on Willian was completed on 28 August.
The 25-year-old Brazilian signed a five-year contract, having moved to England from Russian club Anzhi Makhachkala. He will wear the number 22 shirt.
On completing his move, Willian said: 'I'm very happy to be here, 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.'
Born on 9 August 1988, in Ribeirao Pires, Willian Borges da Silva played at Sao Paulo before moving to Corinthians at the age of nine.
Having made his way through the Brazilian club's academy, Willian rose to prominence in 2005 at the prestigious Copa Sao Paulo de Futebol Junior tournament, which he won with Corinthians before being promoted to the first team shortly after.
Having impressed potential suitors with his performances, Willian's stock continued to rise, culminating in a move to Ukrainian side Shakhtar Donetsk in August 2007.
Possessing trademark Brazilian skills, and with the guile and creativity to unlock tight defences, during his time at Shakhtar Willian won four league titles, three Ukrainian Cups, three Ukrainian Super Cups and, most memorably, the 2009 UEFA Cup, which was clinched with a 2-1 over Werder Bremen.
Chelsea supporters will be familiar with the player after he scored twice at Stamford Bridge when we beat Shakhtar 3-2 in the group stages of last season's Champions League. He also impressed during our 2-1 defeat in the away game.
Willian spent six years at Shakhtar before completing a switch to Anzhi last January.
He made his debut for the club during a 3-1 Europa League win over Hannover and scored his first goal in a 3-0 victory at VN Novgorod.
On the international stage, Willian has been involved with the Brazilian national side at Under-17, Under-18 and Under-20 level, and featured in the FIFA Under-20 World Cup in 2007, when Brazil were eliminated in the quarter-finals by Spain.
He made his Brazil senior debut on 10 November 2011 in a friendly match against Gabon and has two caps. He became the sixth current Chelsea player from that country.