Exploiting high-performance electrolyte holds the key for realization practical application of rechargeable magnesium batteries (RMBs). Herein, a new non-nucleophilic mononuclear electrolyte was developed and its electrochemical active species was identified as [Mg(DME)₃][GaCl₄]₂ through single-crystal X-ray diffraction analysis. The as-synthesized Mg(GaCl₄)₂-IL-DME electrolyte could achieve a high ionic conductivity (9.85 mS cm⁻¹), good anodic stability (2.9 V vs. Mg/Mg²⁺), and highly reversible Mg plating/stripping. The remarkable electrochemical performance should be attributed to the in-situ formation of Mg²⁺-conducting Ga₅Mg₂ alloy layer at the Mg/electrolyte interface during electrochemical cycling, which not only efficiently protects the Mg anode from passivation, but also allows for rapid Mg-ion transport. Significantly, the Mg(GaCl₄)₂-IL-DME electrolyte showed excellent compatibility with both conversion and intercalation cathodes. The Mg/S batteries with Mg(GaCl₄)₂-IL-DME electrolyte and KB/S cathode showed a high specific capacity of 839 mAh g⁻¹ after 50 cycles at 0.1 C with the Coulombic efficiency of ~100%. Moreover, the assembled Mg||Mo₆S₈ batteries delivered a reversible discharge capacity of 85 mAh g⁻¹ after 120 cycles at 0.2 C. This work provides a universal electrolyte for the realization of high-performance and practical RMBs, especially Mg/S batteries.