The 26-year-old Tunisia international has moved to St Andrew's from Spanish side Racing Santander on an initial season long loan deal with a view to making the move a permanent one at the end of the season.
Blues hope to have international clearance on Nafti in time for him to come in to contention for a place in manager Steve Bruce's squad for the game against Southampton at St Andrew's on Wednesday evening.
Nafti is Blues' third transfer window loan signing which is allowed because the maximum two-loan rule only applies to deals between British clubs.