Controlling magnetism by an electric field is of critical importance for the future development of ultralow-power electronic and spintronic devices. Progress has been made in electrically driven nonvolatile tuning of magnetic states in multiferroic heterostructures for the information storage industry, which is exclusively attributed to the ferroelectric-polarization-switching-induced interfacial charge effect or nonlinear lattice strain effect. Here, we demonstrate that a hitherto unappreciated shear strain in the ferroelectric 0.7Pb(Mg1/3Nb2/3)O3–0.3PbTiO3 substrate triggered by an electric field can be adopted to obtain robust nonvolatile control of the ferromagnetic resonance in an elastically coupled epitaxial Fe70Rh30 thin film. The disappearance of the resonance peak in a low-field-sweeping mode and the large resonance field shift of 111 Oe upon polarization switching demonstrate a strong shear-strain-mediated magnetoelectric coupling effect. In particular, in situ Kerr measurement identifies that the nonvolatile magnetic switching purely originates from electric-field-induced 109° ferroelastic domain switching rather than from 71°/180° ferroelectric domain switching even without the assistance of a magnetic field. This discovery illustrates the role of shear strain in achieving electrically tunable nonvolatile modulation of dynamic magnetic properties, and favors the design of future energy-efficient magnetoelectric microwave devices.