The stability and post-bifurcation of a non-linear magnetoelastic film/substrate block is experimentally exploited to obtain active control of surface roughness. The non-intuitive interplay between magnetic field and elastic deformation owes to material and geometry selection, namely a ferromagnetic particle composite film bonded on a compliant passive foundation. Cooperation of the two otherwise independent loading mechanisms-mechanical pre-compression and magnetic field-allows one to bring the structure near a marginally stable state and then destabilize it with either magnetic or mechanical fields. We demonstrate for the first time that the critical magnetic field is a decreasing function of pre-compression and vice versa. The experimental results are then probed successfully with full-field finite element simulations at large strains and magnetic fields. The magnetoelastic coupling allows for reversible on/off control of surface wrinkling under adjustable critical magnetic and mechanical fields, thus this study constitutes a first step towards realistic active haptic and morphing devices.