The remarkable chemical durability of silicate glass makes it suitable for a wide range of applications. The slowdown of the aqueous glass corrosion kinetics that is frequently observed at long time is generally attributed to chemical affinity effects (saturation of the solution with respect to silica). Here, we demonstrate a new mechanism and highlight the impact of morphological transformations in the alteration layer on the leaching kinetics. A direct correlation between structure and reactivity is revealed by coupling the results of several structure-sensitive experiments with numerical simulations at mesoscopic scale. The sharp drop in the corrosion rate is shown to arise from densification of the outer layers of the alteration film, leading to pore closure. The presence of insoluble elements in the glass can inhibit the film restructuring responsible for this effect. This mechanism may be more broadly applicable to silicate minerals.