Recent advances in phase transition transduction enabled the design of a non-resonant broadband mechanical energy harvester that is capable of delivering an energy density per cycle up to two orders of magnitude larger than resonant cantilever piezoelectric type generators. This was achieved in a [011] oriented and poled domain engineered relaxor ferroelectric single crystal, mechanically biased to a state just below the ferroelectric rhombohedral (F R )-ferroelectric orthorhombic (F O ) phase transformation. Therefore, a small variation in an input parameter, e.g., electrical, mechanical, or thermal will generate a large output due to the significant polarization change associated with the transition. This idea was extended in the present work to design a non-resonant, multi-domain magnetoelectric composite hybrid harvester comprised of highly magnetostrictive alloy, [Fe 81.4 Ga 18.6 (Galfenol) or Tb x Dy 1´x Fe 2 (Terfenol-D)], and lead indium niobate-lead magnesium niobate-lead titanate (PIN-PMN-PT) domain engineered relaxor ferroelectric single crystal. A small magnetic field applied to the coupled device causes the magnetostrictive element to expand, and the resulting stress forces the phase change in the relaxor ferroelectric single crystal. We have demonstrated high energy conversion in this magnetoelectric device by triggering the F R -F O transition in the single crystal by a small ac magnetic field in a broad frequency range that is important for multi-domain hybrid energy harvesting devices.