Rechargeable magnesium batteries (RMBs) employing conventional ether-based electrolytes often suffer from sluggish interfacial kinetics, which primarily originate from the strong solvation of divalent Mg$^{2+}$ ions and the resultant high desolvation energy barrier. In this work, we rationally modulate the Mg$^{2+}$ solvation structure by introducing a simple amine additive, isobutylamine (IBA), which loosens the primary solvation sheath by partially displacing ether solvents and facilitating anion participation in the solvation shell. This reconstructed solvation environment, enriched with nitrogen and fluorine, promotes the formation of an inorganic-rich solid electrolyte interphase (SEI) containing magnesium nitride and magnesium fluoride, as confirmed by systematic characterization. Owing to the reduced ionic transport barrier within the SEI, the IBA-modified electrolyte exhibits a higher Mg$^{2+}$ transference number and a higher exchange current density compared to the baseline ether electrolyte. Consequently, the cyclic stability of the Mg anode is significantly extended from 120 h to 1800 h, representing a fifteen-fold improvement. These findings underscore the effectiveness of rational solvation structure engineering and highlight IBA as a promising additive for developing high-performance magnesium electrolytes.