Based on the embedded-atom method (EAM), an analytical effective potential is developed to model the interaction of a metallic adsorbate on a perfect crystalline substrate, which is also metallic. The many-body character of the original EAM potential is preserved in the adsorbate energy and in the alteration of the substrate energy due to the presence of the adsorbate. A mean-field-type version neglecting corrugation of the substrate is first derived based on rigorous integration of individual monolayers, followed by an approximate form for the perturbation of the substrate energy. Lateral corrugation is subsequently included by additional phenomenological terms respecting the symmetry of the substrate, again preserving the many-body nature of the original potential. The effective model contains four parameters to describe uncorrugated substrates and eight extra parameters to describe every order of the Fourier lateral expansion. These parameters were fitted to reproduce the adsorption energy of a sample of random configurations of realistic 2D and 3D clusters deposited on the (1 1 1) fcc surface, for metals for which popular EAM models have been parametrized. As a simple application, the local relaxation of pre-formed icosahedral or truncated octahedral clusters soft-landed and exposing (1 1 1) faces in epitaxy to the substrate has been simulated at 0 and 300 K. The deformation of small clusters to wet the substrate is correctly captured by the effective model. This agreement with the exact potential suggests that the present model should be useful for treating metallic environments in large-scale surface studies, notably in structural optimization or as a template for more general models parametrized from ab initio data.