Quantum effects of plasmonic phenomena have been explored through ab initio studies, but only for exceedingly small metallic nanostructures, leaving most experimentally relevant structures too large to handle. We propose instead an effective description with the computationally appealing features of classical electrodynamics, while quantum properties are described accurately through an infinitely thin layer of dipoles oriented normally to the metal surface. The nonlocal polarizability of the dipole layer-the only introduced parameter-is mapped from the free-electron distribution near the metal surface as obtained with 1D quantum calculations, such as time-dependent density-functional theory (TDDFT), and is determined once and for all. The model can be applied in two and three dimensions to any system size that is tractable within classical electrodynamics, while capturing quantum plasmonic aspects of nonlocal response and a finite work function with TDDFT-level accuracy. Applying the theory to dimers, we find quantum corrections to the hybridization even in mesoscopic dimers, as long as the gap itself is subnanometric.