Birmingham boss Lee Clark said the teenage midfielder had the potential to break into the club's first-team this season.
Nabay has moved after handing in a transfer request and compensation, believed to be in the region of £200,000, has been agreed between the two clubs.
Clark said: "I made it clear to Foday in several meetings with him that he had the potential to become the youngest-ever player to appear for Birmingham City's first-team this season.
"That's how highly I rated him. And how highly the club rated him. I wanted him to stay but as a football manager I couldn't have done any more."