The adsorption of silver and gold atoms, and M-2, M-6, and M-13 (M = Ag or An) clusters on the (0001) graphite surface has been investigated computationally using the density functional theory (DFT) with periodic boundary conditions and plane wave basis functions. The surface has been modeled as a single carbon sheet. The role of dispersion forces has been studied with an empirical classical model. The results show that the clusters avoid hollow sites on the graphite surface, and that the metal atoms favor atop and bond sites. Large structural changes are observed in octahedral M-6 and icosahedral M-13 clusters on the graphite surface when compared with gas-phase geometries. The results also indicate that if accurate results are required, the dispersion forces between metal and carbon atoms should be included in the studied systems.