Scanning tunneling microscopy and low energy electron diffraction show that high quality fcc Ni(111) films can be prepared on W(110). The subsequent coverage of this Ni template by monolayers of Fe leads to a Fe/Ni bilayer with striking magnetic properties. The Fe cap layer induces a spin reorientation of the easy axis of magnetization from in-plane to perpendicular to the film, as checked with the magneto-optic Kerr effect. At higher Fe coverages, an in-plane magnetization of the bilayer is found, which is proposed to be caused by the fcc to bcc transition in the Fe layer.