Fluoride ion batteries are potential "next-generation" electrochemical storage devices that offer high energy density. At present, such batteries are limited to operation at high temperatures because suitable fluoride ion-conducting electrolytes are known only in the solid state. We report a liquid fluoride ion-conducting electrolyte with high ionic conductivity, wide operating voltage, and robust chemical stability based on dry tetraalkylammonium fluoride salts in ether solvents. Pairing this liquid electrolyte with a copper-lanthanum trifluoride (Cu@LaF3) core-shell cathode, we demonstrate reversible fluorination and defluorination reactions in a fluoride ion electrochemical cell cycled at room temperature. Fluoride ion-mediated electrochemistry offers a pathway toward developing capacities beyond that of lithium ion technology.