The quest for higher data density in information storage is motivating investigations into approaches for manipulating magnetization by means other than magnetic fields. This is evidenced by the recent boom in magnetoelectronics and 'spintronics', where phenomena such as carrier effects in magnetic semiconductors and high-correlation effects in colossal magnetoresistive compounds are studied for their device potential. The linear magnetoelectric effect-the induction of polarization by a magnetic field and of magnetization by an electric field-provides another route for linking magnetic and electric properties. It was recently discovered that composite materials and magnetic ferroelectrics exhibit magnetoelectric effects that exceed previously known effects by orders of magnitude, with the potential to trigger magnetic or electric phase transitions. Here we report a system whose magnetic phase can be controlled by an external electric field: ferromagnetic ordering in hexagonal HoMnO3 is reversibly switched on and off by the applied field via magnetoelectric interactions. We monitor this process using magneto-optical techniques and reveal its microscopic origin by neutron and X-ray diffraction. From our results, we identify basic requirements for other candidate materials to exhibit magnetoelectric phase control.