We demonstrate that the growth of Fe/(Ga,Mn)As heterointerfaces can be efficiently controlled by epitaxy and that robust ferromagnetism of the interfacial Mn atoms is induced at room temperature by the proximity effect. X-ray magnetic circular dichroism and x-ray resonant reflectivity data, supported by theoretical calculations, were used to monitor both temperature and magnetic field dependence of the Mn magnetic moment in the semiconducting host. We identify distinct Mn populations, each of them with specific magnetic character.