An average-atom (A-atom) embedded-atom-method potential for random multicomponent alloys at any composition is derived analytically and validated by comparing A-atom and true random alloys bulk and defect properties, in model Fe-Ni-Cr systems. The A-atom can be mixed with the individual alloying-element potentials, thus enabling computation of defect/defect interactions. Its use provides quantitative insight into the physical role of the fluctuations, and has many applications, such as in atomistic/continuum modeling of random alloys and the development of new potentials with controlled properties.