Details of the mechanism of asymmetric transfer hydrogenation of ketones catalyzed by two chiral bifunctional ruthenium complexes, (S)-RuH[(R,R)-OCH(Ph)CH(Ph)NH(2)](η(6)-benzene) (Ru-1) or (S)-RuH[(R,R)-p-TsNCH(Ph)CH(Ph)NH(2)](η(6)-mesitylene) (Ru-2), were studied computationally by density functional theory, accounting for the solvation effects by using continuum, discrete, and mixed continuum/discrete solvation models via "solvated supermolecules" approach. In contrast to gas phase quantum chemical calculations, where the reactions were found to proceed via a concerted three-bond asynchronous process through a six-membered pericyclic transition state, incorporation of the implicit and/or explicit solvation into the calculations suggests that the same reactions proceed via two steps in solution: (i) enantio-determining hydride transfer and (ii) proton transfer through the contact ion-pair intermediate, stabilized primarily by ionic hydrogen bonding between the cation and the anion. The calculations suggest that the proton source for neutralizing the chiral RO(-) anion may be either the amine group of the cationic Ru complex or, more likely, a protic solvent molecule. In the latter case, the reaction may not necessarily proceed via the 16e amido complex Ru[(R,R)-XCH(Ph)CH(Ph)NH](η(6)-arene). The origin of enantioselectivity is discussed in terms of the newly formulated mechanism.