This paper proposes and implements biophysical constraints to select a unique solution to the bioelectromagnetic inverse problem. It first shows that the brain's electric fields and potentials are predominantly due to ohmic currents. This serves to reformulate the inverse problem in terms of a restricted source model permitting noninvasive estimations of Local Field Potentials (LFPs) in depth from scalp-recorded data. Uniqueness in the solution is achieved by a physically derived regularization strategy that imposes a spatial structure on the solution based upon the physical laws that describe electromagnetic fields in biological media. The regularization strategy and the source model emulate the properties of brain activity's actual generators. This added information is independent of both the recorded data and head model and suffices for obtaining a unique solution compatible with and aimed at analyzing experimental data. The inverse solution's features are evaluated with event-related potentials (ERPs) from a healthy subject performing a visuo-motor task. Two aspects are addressed: the concordance between available neurophysiological evidence and inverse solution results, and the functional localization provided by fMRI data from the same subject under identical experimental conditions. The localization results are spatially and temporally concordant with experimental evidence, and the areas detected as functionally activated in both imaging modalities are similar, providing indices of localization accuracy. We conclude that biophysically driven inverse solutions offer a novel and reliable possibility for studying brain function with the temporal resolution required to advance our understanding of the brain's functional networks.