Details of the move from Siena and Coulibaly's contract have not yet been revealed.
A statement on the club's website said: "We are delighted to announce that we have reached agreement with Souleymane Coulibaly to join the club."
The 16-year-old striker hit nine goals in four games for the Ivory Coast during the recent Under-17 World Cup in Mexico, including a hat-trick against Brazil and four against Denmark.
This secured the golden boot and equalled the tournament record set by former Liverpool striker Florent Sinama Pongolle, who achieved the milestone with three more games ten years ago.
Coulibaly's playing style has led to the teenager being compared to Chelsea striker and compatriot Didier Drogba.
He was linked with moves to many of Europe's leading clubs, including Real Madrid, after his scoring run in Mexico.