Multivariate generalized Gaussian distributions (MGGDs) have aroused a great interest in the image processing community thanks to their ability to describe accurately various image features, such as image gradient fields. However, so far their applicability has been limited by the lack of a transformation between two of these parametric distributions. In this paper, we propose a novel transformation between MGGDs, consisting of an optimal transportation of the second-order statistics and a stochastic-based shape parameter transformation. We employ the proposed transformation between MGGDs for a color transfer and a gradient transfer between images. We also propose a new simultaneous transfer of color and gradient, which we apply for image color correction.