We report on ferroelectric field effect experiments in ultrathin layers of the metallic perovskite SrRuC<3 using Pb(Zr0.52Ti0.48)O3/SrRuO3 epitaxial heterostructures. Switching the ferroelectric polarization of the Pb(Zr0.52Ti0.48)O3 layer induces a ∼ 10% change in the sheet resistance of the SrRuO3 layer that is nonvolatile and also reversible. Hall effect measurements that take into account the anomalous Hall effect reveal a carrier concentration of n ∼ 2 × 1022 electrons/cm3 and allow us to understand quantitatively the sign and magnitude of the observed resistance change. Of key importance for these experiments is the crystalline and surface quality of the SrRuO3 and Pb(Zr0.52Ti0.48)O3 layers. We also discuss how this general approach of nonvolatile doping using ferroelectrics opens new possibilities of directly creating small electronic structures without using traditional lithographic techniques.