An unexplored physical mechanism which produces a magnetoelectric effect in ferroelectric-ferromagnetic multilayers is studied based on first-principles calculations. Its origin is a change in bonding at the ferroelectric-ferromagnet interface that alters the interface magnetization when the electric polarization reverses. Using Fe/BaTiO3 multilayers as a representative model, we show a sizable difference in magnetic moments of Fe and Ti atoms at the two interfaces dissimilar by the orientation of the local electric dipole moments. The predicted magnetoelectric effect opens a new direction to control magnetic properties of thin-film layered structures by electric fields.