We report photoemission experiments revealing the full valence electron spectral function of Ce adatoms on Ag(111), W(110), and Rh(111) surfaces. A transfer of Ce 4f spectral weight from the ionization peak towards the Fermi level is demonstrated upon changing the substrate from Ag(111) to Rh(111). In the intermediate case of Ce on W(110) the ionization peak is found to be split. This evolution of the spectra is explained by means of first-principles theory, which clearly demonstrates that a reliable understanding of magnetic adatoms on metal surfaces requires simultaneous low and high energy spectroscopic information.