Rechargeable magnesium and calcium metal batteries (RMBs and RCBs) are promising alternatives to lithium-ion batteries because of the high crustal abundance and capacity of magnesium and calcium. Yet, they are plagued by sluggish kinetics and parasitic reactions. We found a family of methoxyethyl-amine chelants that greatly promote interfacial charge transfer kinetics and suppress side reactions on both the cathode and metal anode through solvation sheath reorganization, thus enabling stable and highly reversible cycling of the RMB and RCB full cells with energy densities of 412 and 471 watt-hours per kilogram, respectively. This work provides a versatile electrolyte design strategy for divalent metal batteries.