We report the resistive switching (RS) characteristics of Al/TiO₂/Au memristive cells fabricated in a crossbar array. The measured R.V curves suggest that RS takes place essentially at the Au/TiO₂ interface. We propose a model based on the electric field enhanced migration of oxygen vacancies at that interface which reproduces the main features of the experimental data, namely the remnant resistance states and the degradation process. Obtained vacancy profiles at the active region of the junction give insight for the design of improved devices.