We demonstrate that a C60 overlayer enhances the perpendicular magnetic anisotropy of a Co thin film, inducing an inverse spin reorientation transition from in plane to out of plane. The driving force is the C60/Co interfacial magnetic anisotropy that we have measured quantitatively in situ as a function of the C60 coverage. Comparison with state-of-the-art ab initio calculations show that this interfacial anisotropy mainly arises from the local hybridization between C60 pz and Co dz2 orbitals. By generalizing these arguments, we also demonstrate that the hybridization of C60 with a Fe(110) surface decreases the perpendicular magnetic anisotropy. These results open the way to tailor the interfacial magnetic anisotropy in organic-material-ferromagnet systems.