Distributed linear solutions have frequently been used to solve the source localization problem in EEG. Here we introduce an approach based on the weighted minimum norm (WMN) method that imposes constraints using anatomical and physiological information derived from other imaging modalities. The anatomical constraints are used to reduce the solution space a priori by modeling the spatial source distribution with a set of basis functions. These spatial basis functions are chosen in a principled way using information theory. The reduced problem is then solved with a classical WMN method. Further (functional) constraints can be introduced in the weighting of the solution using fMRI brain responses to augment spatial priors. We used simulated data to explore the behavior of the approach over a range of the model's hyperparameters. To assess the construct validity of our method we compared it with two established approaches to the source localization problem, a simple weighted minimum norm and a maximum smoothness (Loreta-like) solution. This involved simulations, using single and multiple sources that were analyzed under different levels of confidence in the priors.