Traore, who made his international debut as a 15-year-old, has long been on the Blues' radar and impressed during their pre-season tour of Asia, when the attacking midfielder scored a spectacular goal in an 8-1 thrashing of the Indonesia All Stars.
Chelsea were unable to sign Traore to a permanent deal until his 18th birthday last month, but a pre-contract agreement was made last year and has now been finalised.
With the opening of the January transfer window, he has now officially moved from Association Jeunes Espoirs De Bobo-Dioulasso in his native Burkina Faso.
Traore made his full international debut in September 2011 a few days before his 16th birthday, and he made a substitute appearance at the 2012 Africa Cup of Nations.
He now hopes to follow in the footsteps of many other Premier League stars: "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."