We used density functional theory (DFT) calculations to model the interaction of hydrogen atoms and molecules with strained bonds and neutral oxygen vacancies in amorphous silica $({\text{a-SiO}}_{2})$. The results demonstrate that the interaction of atomic hydrogen with strained Si--O bonds in defect-free ${\text{a-SiO}}_{2}$ networks results in the formation of two distinct defect structures, which are referred to as the ${[{\text{SiO}}_{4}/\text{H}]}^{0}$ and the hydroxyl ${\text{E}}^{\ensuremath{'}}$ center. To study the distribution of each defect's properties, up to 116 configurations of each center were calculated. We show that the hydroxyl ${E}^{\ensuremath{'}}$ center can be thermodynamically stable in the neutral charge state. In order to understand the origins and reactions of this defect, different mechanisms of formation, passivation, and depassivation have been investigated. The interaction of H with a single-oxygen vacancy in ${\text{a-SiO}}_{2}$ was studied in 144 configurations, all resulting in the hydrogen bridge defect. The reaction of the hydrogen bridge defect with the second H atom is barrierless and fully passivates the O vacancy. The latter defect reacts with atomic H with a small barrier, restoring the hydrogen bridge defect. These results provide a better understanding of how atomic and molecular hydrogen can both passivate existing defects and create new electrically active defects in amorphous-silica matrices.