Electrolytes with anion-rich solvated structures are promising for high-voltage lithium metal batteries (LMBs) due to their good interfacial compatibility. Nevertheless, limited Li-ion transport of these electrolytes has hindered their high-rate application. Here we demonstrate that Li-ion transport in anion-rich solvated electrolytes could be facilitated by designing the coordination topology of anions in the solvation structure. Results show that, for a binary-anion electrolyte, equal-molar anions show the most expanded energy level distribution of solvation structures, thus reducing the Li-ion transport energy barrier, and resulting in a Li-ion conductivity even higher than that of the commercial carbonate electrolyte at a temperature range from -40 °C to 60 °C. More importantly, we identify a universal principle governing the Li-ion transport enhancement driven by anion configurations: only the combination of anions with multi-coordination sites shows facilitation in Li-ion transport, while the combination of centrosymmetric anions with the mono-coordination site harms it. The diversified anion-rich solvated structures also form stable interphases on the electrodes, enabling long-term cycling of 4.5 V LMBs at a high current density of 3.78 mA cm-2. Overall, our findings shine new light on developing practical electrolytes for energy-dense LMBs.