The Brazilian completed his £32 million move from Russian side Anzhi on Wednesday upon securing a work permit, having joined his new club after completing a medical at London rivals Tottenham.
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"Finally it's become a reality, and when the offer came I never gave a thought to anybody else, I said to myself that I would run here, and I'm happy to be here now. Chelsea was always my first choice.
"It's going to be an immense pleasure to work with Jose Mourinho, listen to him and learn from him. I'm sure I'm going to grow as a professional and I'm looking forward to training," he continued.
"He's one of the best coaches in the world with everything he's won. I'm sure I'm going to learn a lot and improve a lot."
Willian is unavailable for Chelsea's Uefa Super Cup clash with Bayern Munich on Friday, so will have to wait until after the international break to make his Blues debut.