We show that charge ordered rare-earth nickelates of the type RNiO3 (R = Ho, Lu, Pr and Nd) are multiferroic with very large magnetically-induced ferroelectric (FE) polarizations. This we determine from first principles electronic structure calculations. The emerging FE polarization is directly tied to the long-standing puzzle of which kind of magnetic ordering is present in this class of materials: its direction and size indicate the type of ground-state spin configuration that is realized. Vice versa, the small energy differences between the different magnetic orderings suggest that a chosen magnetic ordering can be stabilized by cooling the system in the presence of an electric field.