This article addresses the under-determined reverberant audio source separation when prior knowledge about the spatial source locations and the room characteristics is available. We consider the Gaussian modeling framework whereby the contribution of each source to all mixture channels in the time-frequency domain is modeled as a zero-mean Gaussian random variable whose covariance represents the spatial characteristics of the source. We advocate the use of rigorous Bayesian estimation by defining three different priors over the spatial parameters, whose means are given by the theory of statistical room acoustics and whose variances are learned from training data. We then derive corresponding Expectation-Maximization (EM) algorithms to estimate the model parameters in the Maximum A Posteriori (MAP) sense. These algorithms provide a principled solution to the well-known permutation problem and two of them achieve better separation performance, as shown in our experiment, than Maximum Likelihood (ML) based EM algorithms exploiting the same prior knowledge.