The structure of glassy GeS2 is studied in the framework of density functional theory, by using a fully self-consistent first-principles molecular dynamics (FPMD) scheme. A comparative analysis is performed with previous molecular dynamics data obtained within the Harris functional (HFMD) total energy approach. The calculated total neutron structure factor exhibits an unprecedented agreement with the experimental counterpart. In particular, the height of the first sharp diffraction peak (FSDP) improves considerably upon the HFMD results. Both the Ge and the S subnetworks are affected by a consistent number of miscoordinations, coexisting with the main tetrahedral structural motif. Glassy GeS2 features a short-range order quite similar to the one found in glassy GeSe2, a notable exception being the larger number of edge-sharing connections. An electronic structure localization analysis, based on the Wannier functions formalism, provides evidence of a more enhanced ionic character in glassy GeS2 when compared to glassy GeS2.