The observation of sharp atomiclike multiplet features is unexpected for individual 3d atoms adsorbed on transition-metal surfaces. However, we show by means of x-ray absorption spectroscopy and x-ray magnetic circular dichroism that individual Fe atoms on Cu(111) exhibit such features. They are reminiscent of a low degree of hybridization, similar to 3d atoms adsorbed on alkali-metal surfaces. We determine the spin, orbital, and total magnetic moments, as well as magnetic anisotropy energy for the individual Fe atoms and for small Fe clusters that we form by increasing the coverage. The multiplet features are smoothened and the orbital moment rapidly decreases with increasing cluster size. For Fe monomers, comparison with density functional theory and multiplet calculations reveals a d(7) electronic configuration, owing to the transfer of one electron from the 4s to the 3d states.