Despite a deal having also been agreed with rivals Tottenham from Russian club Anzhi Makhachkala, the 25-year-old opted to instead join the Blues under new manager Jose Mourinho.
It is an opportunity the creative forward intends to meet full-on as he looks to force his way into contention with the likes of Eden Hazard, Oscar, Juan Mata, Ramires, Andre Schurrle and Kevin De Bruyne as he stakes his claim for a spot in the Brazil national team next summer.
"I will train, play and do my best to get the trust of the manager and of the fans.
"There is no doubt English football is very big, with huge visibility. I hope that helps me to be called up for the national team - but of course that depends on me.
"I will have to play and prove I deserve that spot. I first have to become a regular starter, then play well and be called up [by Brazil], this is my goal."
Chelsea have long tracked Willian, with Mourinho, who returned to Stamford Bridge earlier this summer, accepting the player would "need a bit of time to express himself" following the transition to the English game.
Willian is relishing the challenges ahead after finally securing his dream move.
"Things just happened. Chelsea came with an offer and everyone knows that I wanted to play for the club since I was at Shakhtar," he added.