Magnetoelectric (ME) composites inherently convert magnetic energy to electrical energy and vice-versa, making them a viable technology in wireless energy transfer (WET) applications. This article focuses on identifying the optimal configuration for achieving relatively high ME power conversion efficiency in a fully ME-based transmitter/receiver composite system. Two configurations of ME composites, one in concentric composite rings and the other in layered laminate formation, have been fabricated and used alternately as transmitters and receivers. The influence of three important parameters has been experimentally studied and reported, including the effect of (1) the magnetization state of the magnetostrictive components and (2) the relative orientation of and (3) the separation distance between the transmitter and the receiver. It has been found that a higher energy conversion efficiency is obtained in a configuration where the laminated plate was used as the transmitter while the ring composites acted as the receiver. Furthermore, the location and alignment of the receiver significantly influence the output transferred power. Lastly, the distance between the transmitter and the receiver has been observed to have an exponential inverse influence on the performance of the investigated WET system. These results have been deciphered by experimentally generating horizontal and vertical magnetic field mapping around the composite systems and capacitance measurement of the piezoelectric element. Thus, this article presents a detailed study of the parameters and their influence on the performance of the ME-based WET technology, which would be extremely useful in designing and optimizing devices based on this technology.