Salzburg says FIFA made a ruling Wednesday after analyzing why the attempted deal missed the Jan. 31 transfer deadline by minutes.
Salzburg sporting director Dietmar Beiersdorfer says all sides had wanted the transfer to happen.
Vittek, who scored four goals at the 2010 World Cup, is among the first players affected by FIFA's new online transfer system.
Deals between clubs from different countries are approved only when both clubs provide matching financial information.
FIFA is still evaluating about 60 blocked transfers.