This paper introduces explicit dependence of atomic polarizabilities on intermolecular interactions within the framework of a polarizable force field AMOEBA. Polarizable models used in biomolecular simulations often poorly describe molecular electrostatic induction in condensed phase, in part, due to neglect of a strong dependency of molecular electronic polarizability on intermolecular interactions at short distances. Our variable polarizability model parameters are derived from quantum chemical calculations of small clusters of atoms and molecules, and can be applied in simulations in condensed phase without additional scaling factors. The variable polarizability model is applied to simulate a ligand exchange reaction for a Mg2+ ion solvated in water. Explicit dependence of water polarizability on a distance between a water oxygen and Mg2+ is derived from in vacuum MP2 calculations of Mg2+-water dimer. The simulations yield a consistent description of the energetics of the Mg2+-water clusters of different size. Simulations also reproduce thermodynamics of ion solvation as well as kinetics of a water ligand exchange reaction. In contrast, simulations that used the additive force field or that used the constant polarizability models were not able to consistently and quantitatively describe the properties of the solvated Mg2+ ion.