The 18-year-old agreed the deal with the west Londoners in October, with the opening of the January transfer window allowing him to make the switch from Association Jeunes Espoirs De Bobo-Dioulasso in his native country.
Traore, a senior international since the age of 15, was taken as a trialist on Chelsea's summer tour of Asia and played a part in all three matches, scoring in Malaysia and Indonesia.
"I'm an attacking midfielder," he told Chelsea TV. "I can play in the number 10 position, I can play on the wings and I'm good on the ball. I can shoot well and am strong in a one v one situation, so I can score goals.
"My favourite players are Juan Mata, Mesut Ozil and Eden Hazard. They're very good players and I am trying to be like them. At Chelsea I look to follow the way of some African legends like Didier Drogba, Michael Essien and now Samuel Eto'o."