Electrolyte solutions including at least one anhydrous fluoride salt and at least one non-aqueous solvent are presented. The fluoride salt includes an organic cation having a charge center (e.g., N, P, S, or O) that does not possess a carbon in the β-position or does not possess a carbon in the β-position having a bound hydrogen. This salt structure facilitates its ability to be made anhydrous without decomposition. Example anhydrous fluoride salts include (2,2-dimethylpropyl)trimethylammonium fluoride and bis(2,2-dimethylpropyl)dimethylammonium fluoride. Combining these fluoride salts with at least one fluorine-containing non-aqueous solvent (e.g., bis(2,2,2-trifluoroethyl)ether; (BTFE)) promotes solubility of the salt within the non-aqueous solvents. The solvent may be a mixture of at least one non-aqueous, fluorine-containing solvent and at least one other non-aqueous, fluorine or non-fluorine containing solvent (e.g., BTFE and propionitrile or dimethoxyethane). The electrolyte solutions may be employed in electrochemical cells, such as batteries, fuel cells, electrolysis systems, and capacitors.