We present direct evidence for room-temperature magnetization reversal induced by an electric field in epitaxial ferroelectric BiFeO3-ferrimagnetic CoFe2O4 columnar nanostructures. Piezoelectric force microscopy and magnetic force microscopy were used to locally image the coupled piezoelectric-magnetic switching. Quantitative analyses give a perpendicular magnetoelectric susceptibility of approximately 1.0 x 10(-2) G cm/V. The observed effect is due to the strong elastic coupling between the two ferric constituents as the result of the three-dimensional heteroepitaxy.