Nanocomposite polymer electrolytes present new opportunities for rechargeable magnesium batteries. However, few polymer electrolytes have demonstrated reversible Mg deposition/dissolution and those that have still contain volatile liquids such as tetrahydrofuran (THF). In this work, we report a nanocomposite polymer electrolyte based on poly(ethylene oxide) (PEO), Mg(BH4)2 and MgO nanoparticles for rechargeable Mg batteries. Cells with this electrolyte have a high coulombic efficiency of 98% for Mg plating/stripping and a high cycling stability. Through combined experiment-modeling investigations, a correlation between improved solvation of the salt and solvent chain length, chelation and oxygen denticity is established. Following the same trend, the nanocomposite polymer electrolyte is inferred to enhance the dissociation of the salt Mg(BH4)2 and thus improve the electrochemical performance. The insights and design metrics thus obtained may be used in nanocomposite electrolytes for other multivalent systems.