Ni nanowires were electrodeposited into track-etched ferroelectric poly(vinylidene difluoride) (PVDF) polymer nanoporous templates to make multiferroic nanostructured composites. Using ferromagnetic resonance measurements under static voltage bias, we demonstrate a magnetoelectric effect arising from a mechanical coupling between the magnetostrictive and piezoelectric phases. The calculated electric field lines and intensity indicate that PVDF matrix surrounding the surface of the Ni nanowires experiences shear stress. The competing magnetoelastic anisotropy originating from the piezoelectric effects leads to a reduced magnetic anisotropy field along the wire axis. The nanowires packing in the array are found to play a dominant role in the magnetoelectric effect.