A magnetoresistive memory cell includes a magnetoresistive layer stack containing a reference layer, a nonmagnetic spacer layer, and a free layer. A ferroelectric material layer having two stable ferroelectric states is coupled to a strain-modulated ferromagnetic layer to alter a sign of magnetic exchange coupling between the strain-modulated ferromagnetic layer and the free layer. The strain-modulated ferromagnetic layer may be the reference layer or a perpendicular magnetic anisotropy layer that is located proximate to the ferroelectric material layer. The magnetoresistive memory cell may be configured as a three-terminal device or as a two-terminal device, and may be configured as a tunneling magnetoresistance (TMR) device or as a giant magnetoresistance (GMR) device.