We have studied the ground-state properties of Ge-related paramagnetic defect centers in Ge-doped silica. Hartree-Fock and density functional theory calculations have been performed to determine the structure, charge, and spin distribution of paramagnetic defects in Ge-doped silica, in particular a trapped electron at a four-coordinated Ge site (GEC) or $[={\mathrm{Ge}}^{\ifmmode\bullet\else\textbullet\fi{}}={]}^{\ensuremath{-}}$ and analogous of the ${E}^{\ensuremath{'}}$ center in silica, ${E}^{\ensuremath{'}}$ Ge or $[\ensuremath{\equiv}{\mathrm{Ge}}^{\ifmmode\bullet\else\textbullet\fi{}}].$ Other possible paramagnetic centers, the dicoordinated Ge lone pair center with a trapped hole $({\mathrm{GLPC}}^{+})$ or $[={\mathrm{Ge}}^{\ifmmode\bullet\else\textbullet\fi{}}{]}^{+}$ and the germyl radical $[\ensuremath{-}{\mathrm{O}\ensuremath{-}\mathrm{G}\mathrm{e}}^{\ifmmode\bullet\else\textbullet\fi{}}=\mathrm{O}]$ are also considered. The corresponding isotropic hyperfine coupling constants have been computed and the assignment of these structures to the observed signals of Ge(1), Ge(2), and Ge(3) centers in silica has been discussed. The calculations support the assignments of the GEC and Ge ${E}^{\ensuremath{'}}$ centers to the Ge(1) and Ge(3) signals.