Large basis set ab initio electronic structure calculations have been carried out to find dipole polarizabilities of over 30 organic molecules containing up to four non-hydrogen atoms. For these molecules, we show that polarizabilities can be divided into transferable atomic contributions. From this demonstration of near-additivity of atomic contributions to the molecular polarizability tenser, a simple predictive scheme emerges. Tests of this scheme on molecules larger than in the original set show that individual tenser elements are predicted to within an average error of around 10% and isotropic polarizabilities have an average error of 3%. As predictions for experimental measurement, we report model values of dipole and quadrupole polarizabilities for certain series of molecules. The near-additivity of atomic contributions we find also has important implications for modeling polarization arising from intermolecular interaction.