We introduce a model that accounts for the bipolar resistive switching phenomenon observed in transition-metal oxides. It qualitatively describes the electric-field-enhanced migration of oxygen vacancies at the nanoscale. The numerical study of the model predicts that strong electric fields develop in the highly resistive dielectric-electrode interfaces leading to spatially inhomogeneous oxygen vacancies distribution and a concomitant resistive switching effect. The theoretical results qualitatively reproduce nontrivial resistance hysteresis experiments that we also report providing key validation to our model.