Using photoemission electron microscopy (PEEM) to image ferromagnetism in polycrystalline Ni disks, and ferroelectricity in their single-crystal BaTiO3 substrates, we find that voltage-driven 90° ferroelectric domain switching serves to reversibly annihilate each magnetic vortex via uniaxial compressive strain, and that the orientation of the resulting bi-domain reveals the chirality of the annihilated vortex. Micromagnetic simulations reveal that only 60% of this strain is required for annihilation. Voltage control of magnetic vortices is novel, and should be energetically favourable with respect to the use of a magnetic field or an electrical current. In future, stray field from bi-domains could be exploited to read vortex chirality. Given that core polarity can already be read via stray field, our work represents a step towards four-state low-power memory applications.