The 25-year-old's switch to the London club on a five-year deal was secured on Wednesday, after being granted a work permit for his transfer from Russian outfit Anzhi Makhachkala.
Fellow Premier League clubs Liverpool and Tottenham were reportedly interested in the midfielder's services, but he opted for a move to Jose Mourinho's side.
And Willian is hopeful the move will benefit him as he looks to become a member of Luiz Felipe Scolari's Brazil squad, at his home World Cup, having previously featured just twice for the national team, in two friendlies in November 2011.
"That is definitely an aim of mine, to win my place in the squad and go to the World Cup," he told the club's official website.
"I will have to work hard for Chelsea to show what I am capable of, and I'm sure if I do that I will have the opportunity to be called up by the national team as a consequence.
"That applies to every player, if you work hard and perform well for your club, you will get those opportunities, and if the chance arrives I want to be ready to take it with both hands."
The former Shakhtar Donetsk player also said he is thrilled by the opportunity to work with Mourinho, and believes his game will improve under the stewardship of the Portuguese manager.
"It's going to be an immense pleasure to work with Jose Mourinho, listen to him and learn from him," he added.
"I'm sure I'm going to grow as a professional and I'm looking forward to training.
"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."
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