Magnetic circular dichroism in valence-band photoemission from perpendicularly magnetized Ni thin films on Cu(001) has been studied both experimentally and theoretically. Over the photon energy range of 11-27 eV for normal emission and normal incidence, intensity asymmetries up to 20% upon light helicity or magnetization direction reversal were found. Fully relativistically calculated photoemission spectra agree well with experiment and reveal the interplay between spin-orbit coupling and exchange splitting, which is at the origin of magnetic dichroism. From comparison of theory and experiment the band dispersion is determined and points of hybridization along the Delta axis are identified.