Structural assignments are determined for Se-77 and Ge-73 chemical shifts through density-functional NMR calculations for GeSe2, Ge4Se9, and GeSe crystals. In particular, a very good agreement between calculated and measured Se-77 isotropic chemical shifts and anisotropies is found for the GeSe2 crystal, for which experimental data are available. These assignments provide a consistent interpretation of experimental Se-77 spectra of GexSe1-x glasses, indicating that the contribution from Ge-Se-Se linkages overlaps with that from Ge-Se-Ge linkages in corner-sharing tetrahedral arrangements, thereby dismissing the occurrence of a bimodal phase.