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 the paperwork has now been completed.
"Traore, joining from Association Jeunes Espoirs De Bobo-Dioulasso, is a full international for Burkina Faso having made his debut in September 2011 a few days before his 16th birthday," a Chelsea statement read.
"He has 10 international caps and has scored once ahead of next month's World Cup qualification play-offs in Africa in which Burkina Faso face Algeria.
"In 2011 he helped his nation win the Africa Under-17s championship.
"An attacking midfielder, Traore was taken as a trialist on Chelsea's tour of Asia in the summer and played a part in all three games, scoring in Malaysia and in Indonesia."
Following his goal in Indonesia during the summer, defender Gary Cahill was full of praise for Traore, saying: "He's a young lad, but I'm sure he's got a bright future at Chelsea."