Chalcogenide glasses with tetrahedral networks can undergo significant densification under pressure owing to their open structures. The structural mechanisms of pressure-induced densification and the corresponding evolution of physical properties of glassy GeSe4 alloy are studied over pressures ranging between ambient and 32.5 GPa, using X-ray scattering supplemented with 3D Monte Carlo structural modeling, Raman spectroscopy, electrical conductivity, and P-V equation of state measurements. The results demonstrate a pressure-induced, hysteretically reversible transition between low-density semiconducting and high-density metallic amorphous phases of GeSe4 near ∼10-15 GPa. These two phases are characterized by their distinct P-V equations of state and structural mechanisms of densification. Densification in the low-density phase is dominated by large inward shifting of the second neighbors with a small amount of conversion from edge-sharing to corner-sharing GeSe4 tetrahedra. On the other hand, densification in the high-density phase involves a gradual increase in the nearest-neighbor coordination numbers of Ge and Se atoms and the formation of Ge-Ge bonds between adjacent polyhedral units. These structural transformations are accompanied by a pressure-induced metallization that is reversible.