The 25-year-old attacker says that Stamford Bridge has always been his preferred destination despite previously completing a medical at Tottenham
The Brazilian completed his €37 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.
"I've always been following Chelsea and every time I came to London I would try to see a Chelsea game and see how the team was doing because it's been my dream to come to play here," he told the club's official website.
"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.