The Visible and near Infrared Hyperspectral Imager (VIHI) is the VIS-IR spectrometer with imaging capabilities aboard the ESA BepiColombo mission to Mercury. In this second paper, we report the instrument spectral characterization derived by the calibration campaign carried out before spacecraft integration. Complementary measurements concerning radiometric and linearity responses, as well as geometric performances, are described in Paper I [G. Filacchione et al., Rev. Sci. Instrum. 88, 094502 (2017)]. We have verified the VIHI spectral range, spectral dispersion, spectral response function, and spectral uniformity along the whole slit. Instrumental defects and optical aberrations due to smiling and keystone effects have been evaluated, and they are lower than the design requirement (<1/3 pixel). The instrumental response is uniform along the whole slit, while spectral dispersion is well represented by a second order curve, rather than to be constant along the spectral dimension.