Pansharpening is a technique that fuses a low spatial resolution multispectral image and a high spatial resolution panchromatic one to obtain a multispectral image with the spatial resolution of the latter while preserving the spectral information of the multispectral image. In this paper we propose a variational Bayesian methodology for pansharpening. The proposed methodology uses the sensor characteristics to model the observation process and Super-Gaussian sparse image priors on the expected characteristics of the pansharpened image. The pansharpened image, as well as all model and variational parameters, are estimated within the proposed methodology. Using real and synthetic data, the quality of the pansharpened images is assessed both visually and quantitatively and compared with other pansharpening methods. Theoretical and experimental results demonstrate the effectiveness, efficiency, and flexibility of the proposed formulation.