The substrate-mediated magnetic interactions between substitutional Co and Fe impurities at the Cu(111) surface have been theoretically investigated as a function of external surface charging. The modification of the interactions as a result of the metallic screening and charge rearrangements are determined self-consistently from first principles by using the Green's-function Korringa-Kohn-Rostoker method. As in the neutral Cu(111) surface, the effective magnetic exchange coupling ∆E between impurities shows Ruderman-Kittel-Kasuya-Yosida-like (RKKY) oscillations as a function of the interimpurity distance. At large interimpurity distances, the wavelength of the RKKY oscillation is not significantly affected by the value and polarity of the external surface charge. Still, important changes in the magnitude of ∆E are observed. For short distances, up to fourth nearest neighbors, surface charging offers remarkable possibilities of controlling the sign and strength of the magnetic coupling. A nonmonotonous dependence of ∆E, including changes from ferromagnetic to antiferromagnetic coupling, is observed as a function of overlayer charging. The charge-induced changes in the surface electronic structure, local magnetic moments, electronic densities of states, and interaction energies are analyzed from a local perspective. The resulting possibilities of manipulating the magnetic interactions in surface nanostructures are discussed.