Among the numerous and interesting features of ionic liquids is their ability to form aqueous biphasic systems (ABSs) when combined with inorganic or organic salts in aqueous media. In this work, a wide range of salts was studied, aiming at gathering a detailed picture on the molecular mechanisms that govern the ability of the salt ions to induce the formation of ionic-liquid-based ABSs. For that purpose, 1-butyl-3-methylimidazolium trifluoromethanesulfonate was chosen due to its facility to undergo liquid-liquid demixing in aqueous media containing conventional salts. The corresponding ternary phase diagrams, tie-lines, and tie-line lengths were determined at 298 K and atmospheric pressure. With the large body of data measured in this work, it was possible to establish a scale on the salt cation and anion abilities to induce the formation of ionic-liquid-based ABSs, which follows the Hofmeister series, and to show that the molar entropy of hydration of the salt ions is the driving force for aqueous two-phase system formation.