The solvation structure of Cu2+ in methanol (MeOH) and dimethyl sulfoxide (DMSO) has been determined by studying both the extended X-ray absorption fine structure (EXAFS) and the X-ray absorption near-edge structure (XANES) regions of the K-edge absorption spectra. The EXAFS technique has been found to provide a very accurate determination of the next-neighbor coordination distances, but it is inconclusive in the determination of the coordination numbers and polyhedral environment. Conversely, quantitative analysis of the XANES spectra unambiguously shows the presence of an average 5-fold coordination in both the MeOH and DMSO solution, ruling out the usually proposed octahedral Jahn-Teller distorted geometry. The EXAFS and XANES techniques provide coherent values of the Cu-O first-shell distances that are coincident in the two solvents. This investigation shows that the combined analysis of the EXAFS and XANES data allows a reliable determination of the structural properties of electrolyte solutions, which is very difficult to achieve with other experimental techniques.