All-oxide magnetic tunnel junctions (MTJs) incorporating functional materials as insulating barriers have the potential of becoming the founding technology for novel multifunctional devices. We investigate, by first-principles density functional theory, the bias-dependent transport properties of an all-oxide SrRuO3/BaTiO3/SrRuO3 MTJ. This incorporates a BaTiO3 barrier which can be found either in a nonferroic or in a ferroelectric state. In such an MTJ not only can the tunneling magnetoresistance reach enormous values, but also, for certain voltages, its sign can be changed by altering the barrier electric state. These findings pave the way for a new generation of electrically controlled magnetic sensors. ; PUBLISHED ; This work is supported by Science Foundation Ireland (Grant No. 07/IN.1/I945), by CRANN and by the EU FP7 ATHENA. Computational resources have been provided by the HEA IITAC project managed by TCHPC and by ICHEC.