Investigations on solid state rechargeable magnesium batteries are considered important similar to lithium batteries. In view of negligible hazards and less reactivity of the magnesium, in comparison with lithium, studies on rechargeable magnesium batteries are expected to have a wide scope in future. Solid polymer electrolytes, which conduct Mg2+ ions and reversibility of a Mg/Mg2+ couple are essential components of the studies. In the present investigations, the existence of reversibility of a Mg/Mg2+ couple in a gel polymer electrolyte (GPE) medium is established for the first time in literature. Results obtained by electrochemical impedance spectroscopy and cyclic voltammetry on Mg/GPE/Mg, SS/GPE/SS symmetrical cells show evidence for the reversibility.