Mg2+ ions are important in biological systems, particularly in stabilizing compact RNA folds. Mg2+ is strongly polarizing, and representing its interactions in heterogeneous environments is a challenge for empirical force field development. To date, the most commonly used force fields in molecular dynamics simulations utilize a pairwise-additive approximation for electrostatic interactions, which cannot account for the significant polarization response in systems containing Mg2+. In the present work, we refine the interactions of Me with water, Cl- ions, and nucleic acid moieties using a polarizable force field based on the classical Drude oscillator model. By targeting gas-phase quantum mechanical interaction energies and geometries of hydrated complexes, as well as condensed-phase osmotic pressure calculations, we present a model for Mg2+ that yields quantitative agreement with experimental measurements of water dissociation free energy and osmotic pressure across a broad range of concentrations. Notable is the direct modeling of steric repulsion between the water Drude oscillators and Mg2+ to treat the Pauli exclusion effects associated with overlap of the electron clouds of water molecules in the first hydration shell around Mg2+. Combined with the refined interactions with nucleic acid moieties, the present model represents a significant advancement in simulating nucleic acid systems containing Mg2+.