We present a general methodology for generating accurate and transferable ab initio force fields, employing the framework of symmetry adapted perturbation theory (SAPT). The resulting force fields are "physically motivated" in that they contain separate, explicit terms to account for the various fundamental intermolecular interactions, such as exchange, electrostatics, induction, and dispersion, with each term parametrized to a corresponding term in the SAPT energy decomposition. Crucially, the resulting force fields are largely compatible with existing, standard simulation packages, requiring only minimal modifications. We present several novel parametrization techniques that yield robust, physically meaningful atomic parameters that are transferable between molecular environments. We demonstrate the accuracy and generality of our method by validating against experimental second virial coefficients for a variety of small molecules. We then show that the resulting atomic parameters can be combined using physically motivated ansatzes to accurately predict arbitrary heteromolecular interaction energies, with example applications including prediction of gas adsorption in functionalized metal-organic framework materials.