The 18-year-old agreed a four-and-a-half-year deal with Jose Mourinho's side back in October and is now a Chelsea player following the opening of the transfer window.
Traore, who made his international debut for Burkina Faso at the age of 15, joins from Association Jeunes Espoirs De Bobo-Dioulasso in his homeland.
Traore impressed as a trialist on Chelsea's tour of Asia in the summer, appearing in all three games and scoring twice.
"It was a good experience with all the senior players and I learned a lot from them," Traore recalled on Chelsea's website.
"I was very proud, so it was a dream for me to be there every day and playing games. Of course I was a little bit nervous but after two or three days I was okay.
"On the pitch I was comfortable, I wasn't nervous once I was on the pitch. Jose Mourniho spoke a lot during training and he is one of the best managers, maybe the best in the world. He is a very good person and it is a dream for me to work with him. I can now say I am living a dream.
"I'm an attacking midfielder. 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."