A non-aqueous Magnesium electrolyte comprising: (a) at least one organic solvent; (b) at least one electrolytically active, soluble, inorganic Magnesium (Mg) salt complex represented by the formula: MgaZbXc wherein a, b, and c are selected to maintain neutral charge of the molecule, and Z and X are selected such that Z and X form a Lewis Acid, and 1≦a≦10, 1≦b≦5, and 2≦c≦30. Further Z is selected from a group consisting of aluminum, boron, phosphorus, titanium, iron, and antimony; X is selected from the group consisting of I, Br, Cl, F and mixtures thereof. Rechargeable, high energy density Magnesium cells containing an cathode, an Mg metal anode, and an electrolyte of the above-described type are also disclosed.