In this work, based on the periodic unfolding homogenization technique, the limiting equations modelling the behaviour of three-dimensional magneto-electro-elastic periodic structures are rigorously established. The local problems and the corresponding homogenized coefficients of the elastic, dielectric, magnetic permittivity, piezoelectric, piezomagnetic and magneto-electric (ME) tensors are explicitly described. The homogenization model is exemplified for laminated composites and a unified general formula for all effective properties of periodic multilaminated magneto-electro-elastic composites is obtained. This formula is applied to investigate the global behaviour for the important case of transversely isotropic constituents and any finite number of layers in each periodic cell. Examples that provide theoretical evidence of the presence of both a product property and the ME effect are given.