We have studied the perpendicular magnetic anisotropy resulting from the L10 chemical ordering of FePd thin films fabricated by Molecular Beam Epitaxy. We show that both the long range order, the directional short range order and the magnetic anisotropy are highly dependant on the deposition conditions. The highest degree of order is obtained with the codeposion of the alloy at 350°C : in this case, the magnetization is perpendicular to the film plane and magnetic domains are formed. Analytical modeling has been used to interpret the variation of the magnetic susceptibility as well as the magnetic domain size with the thickness of the film. We also show that the Mössbauer and Kerr signals are highly dependant on the degree of order of the alloys.