Controlling magnetism by means of electric fields is a key issue for the future development of low-power spintronics(1). Progress has been made in the electrical control of magnetic anisotropy(2), domain structure(3,4), spin polarization(5,6) or critical temperatures(7,8). However, the ability to turn on and off robust ferromagnetism at room temperature and above has remained elusive. Here we use ferroelectricity in BaTiO3 crystals to tune the sharp metamagnetic transition temperature of epitaxially grown FeRh films and electrically drive a transition between antiferromagnetic and ferromagnetic order with only a few volts, just above room temperature. The detailed analysis of the data in the light of first-principles calculations indicate that the phenomenon is mediated by both strain and field effects from the BaTiO3. Our results correspond to a magnetoelectric coupling larger than previous reports by at least one order of magnitude and open new perspectives for the use of ferroelectrics in magnetic storage and spintronics.