We present a density functional study of the structural and electronic properties of small Cu_n (n=1-4) aggregates on defect-free MgO(100). The calculations employ a slab geometry with periodic boundary conditions, supercells with up to 76 atoms, and include full relaxation of the surface layer and of all adsorbed atoms. The preferred adsorption site for a single Cu adatom is on top of an oxygen atom. The adsorption energy and Cu-O distance are 0.99 eV and 2.04 A using the Perdew-Wang gradient corrected exchange correlation functional. The saddle point for surface diffusion is at the "hollow" site, with a diffusion barrier of 0.45 eV. For the adsorbed copper dimer, two geometries, one parallel and one perpendicular to the surface, are very close in energy. For the adsorbed Cu_3, a linear configuration is preferred to the triangular geometry. As for the free cluster, the most stable adsorbed geometry for Cu_4 is a rhombus. The adsorption energy per Cu atom decreases with increasing the size of the cluster, while the Cu-Cu cohesive energy increases, rapidly becoming more important than the adsorption energy.