Strong interest in resistive switching phenomena is driven by a possibility to develop electronic devices with novel functional properties not available in conventional systems. Bistable resistive devices are characterized by two resistance states that can be switched by an external voltage. Recently, memristors-electric circuit elements with continuously tunable resistive behavior-have emerged as a new paradigm for nonvolatile memories and adaptive electronic circuit elements. Employment of memristors can radically enhance the computational power and energy efficiency of electronic systems. Most of the existing memristor prototypes involve transition metal oxide resistive layers where conductive filaments formation and/or the interface contact resistance control the memristive behavior. In this paper, we demonstrate a new type of memristor that is based on a ferroelectric tunnel junction, where the tunneling conductance can be tuned in an analogous manner by several orders of magnitude by both the amplitude and the duration of the applied voltage. The ferroelectric tunnel memristors exhibit a reversible hysteretic nonvolatile resistive switching with a resistance ratio of up to 10(5) % at room temperature. The observed memristive behavior is attributed to the field-induced charge redistribution at the ferroelectric/electrode interface, resulting in the modulation of the interface barrier height.