Silicate glasses are durable materials, but are they sufficiently durable to confine highly radioactive wastes for hundreds of thousands years? Addressing this question requires a thorough understanding of the mechanisms underpinning aqueous corrosion of these materials. Here we show that in silica-saturated solution, a model glass of nuclear interest corrodes but at a rate that dramatically drops as a passivating layer forms. Water ingress into the glass, leading to the congruent release of mobile elements (B, Na and Ca), is followed by in situ repolymerization of the silicate network. This material is at equilibrium with pore and bulk solutions, and acts as a molecular sieve with a cutoff below 1 nm. The low corrosion rate resulting from the formation of this stable passivating layer enables the objective of durability to be met, while progress in the fundamental understanding of corrosion unlocks the potential for optimizing the design of nuclear glass-geological disposal.