We demonstrate that a C(60) 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 (60)/Co interfacial magnetic anisotropy that we have measured quantitatively in situ as a function of the (60) coverage. Comparison with state-of-the-art ab initio calculations show that this interfacial anisotropy mainly arises from the local hybridization between (60) p(z) and Co d(z(2)) orbitals. By generalizing these arguments, we also demonstrate that the hybridization of (60) 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.