The quantum confinement of surface-state electrons in atomic-scale nanostructures is studied by means of the Korringa-Kohn-Rostoker (KKR) Green's function method. We demonstrate that the surface-state mediated interaction between adatoms can be significantly modified by the quantum confinement of surface electrons. We show that quantum corrals and quantum mirrors constructed on metal surfaces can be used to tailor the exchange interaction between magnetic adatoms at large distances. We discuss the self-organization of adatoms on metal surfaces caused by quantum confinement.