Magnetic resonance spectroscopic imaging (MRSI) is a non-invasive technique able to provide the spatial distribu- tion of relevant biochemical compounds commonly used as biomarkers of disease. Information provided by MRSI can be used as a valuable insight for the diagnosis, treatment and follow-up of several diseases such as cancer or neurological disorders. Obtaining accurate metabolite concentrations from in vivo MRSI signals is a crucial require- ment for the clinical utility of this technique. Despite the numerous publications on the topic, accurate quantification is still a challenging problem due to the low signal-to-noise ratio of the data, overlap of spectral lines and the pres- ence of nuisance components. We propose a novel quantification method, which alleviates these limitations by exploiting a spatio-spectral regularization scheme. In contrast to previous methods, the regularization terms are not expressed directly on the parameters being sought, but on appropriate transformed domains. In order to quan- tify all signals simultaneously in the MRSI grid, while introducing prior information, a fast proximal optimization al- gorithm is proposed. Experiments on synthetic MRSI data demonstrate that the error in the estimated metabolite concentrations is reduced by a mean of 41% with the proposed scheme. Results on in vivo brain MRSI data show the benefit of the proposed approach, which is able to fit overlapping peaks correctly and to capture metabolites that are missed by single-voxel methods due to their lower concentrations.