Pansharpening refers to the fusion process of inferring a high-resolution multispectral image from a high-resolution panchromatic image and a low-resolution multispectral one. In this paper we propose a new variational method for pansharpening which incorporates a nonlocal regularization term and two fidelity terms, one describing the relation between the panchromatic image and the high-resolution spectral channels and the other one preserving the colors from the low-resolution modality. The nonlocal term is based on the image self-similarity principle applied to the panchromatic image. The existence and uniqueness of minimizer for the described functional is proved in a suitable space of weighted integrable functions. Although quite successful in terms of relative error, state-of-the-art pansharpening methods introduce relevant color artifacts. These spectral distortions can be significantly reduced by involving the image self-similarity. Extensive comparisons with state-of-the-art algorithms are performed.