The Brazil international, who has signed from Russian side Anzhi Makhachkala, believes that he is joining a "sensational" club.
The 25-year-old told Sportv: "It's a big club, a sensational club. Chelsea have won many titles in the past few years, the Champions League and the Europa League.
"It has great players, with an impressive history, and of course, it has Mourinho. For sure, it is a club that I am happy to play for. It's a dream come true."
Willian could feature when Chelsea travel to Goodison Park to play Everton after the international break.