The Spanish giants were originally sanctioned by world football's governing body in January but their punishments were provisionally lifted pending this appeal.
That enabled them to register new players in the most recent transfer window but they are now banned from doing so in the next two windows.
Atletico and Real have also been fined £696,000 and £278,000 respectively, although Real have already announced that they will appeal against FIFA's ruling at the Court of Arbitration for Sport.
A FIFA statement said: "The FIFA appeal committee has decided to reject the appeals lodged by Spanish clubs Atletico de Madrid and Real Madrid and to confirm in their entirety the decisions rendered by the FIFA disciplinary committee in the respective cases relating to the protection of minors."
It added that the ban "prevents them from registering any players at national and international level for the next two complete and consecutive registration periods" but does not stop them releasing players. It also does not apply to clubs' beach soccer, futsal or women's teams.
Real Madrid, who beat Atletico on penalties in May's Champions League Final, said it would ask the Swiss-based CAS for an urgent appeal hearing.
"We regret this decision on the ground that is profoundly unfair and contrary to the most elementary principles of penal law," a club statement added.
A similar statement from Atletico arrived a few minutes later, confirming that they will also take their case to sport's highest court.