The 25-year old spent just eight months in Russia with Anzhi Makhachkala, where he made 15 appearances before opting for a Premier League switch this summer.
Willian looked set to be joining Tottenham, only for Jose Mourinho to swoop to secure his services, although he revealed he had been aware of the Blues' pursuit for a while.
"They made an offer two months ago but I was not allowed to leave," he told Brazilian television station Sportv.
"I kept following the club and I used to go to London to follow Chelsea whenever I had free time and now my dream has come true.
"I will work with Mourinho who is the best manager and I will grow a lot with him."
Willian will face stiff competition for a place in the team with the likes of Eden Hazard, Oscar, Juan Mata, Ramires, Andre Schurrle and Kevin De Bruyne amongst the names vying for a spot, something which he acknowledged.
"They are quality players and nobody can take their place for granted. So I have to work hard to get a place in the first team," he said.
"Other clubs were interested, but my intention and dream of playing for Chelsea made the difference.
"The opportunity to play with Mourinho, the best manager in the world, also made a lot of difference. I always dreamed of wearing Chelsea's jersey."
Willian also admitted that he hopes the move will boost his chances of making the Brazil squad for next year's World Cup.
"It's my objective - I want to play in the World Cup, be among the 23 players in the squad. It's a dream I have and order to achieve it, I need to have a great season at Chelsea," he said.
"I want to play for the national team. I had a chance to when Mano Menezes was the manager and I hope to have with Scolari too. But I have to work hard and do my best every game."