Future increases in stratospheric water vapour risk amplifying climate change and slowing down the recovery of the ozone layer. However, state-of-the-art climate models strongly disagree on the magnitude of these increases under global warming. Uncertainty primarily arises from the complex processes leading to dehydration of air during its tropical ascent into the stratosphere. Here we derive an observational constraint on this longstanding uncertainty. We use a statistical-learning approach to infer historical co-variations between the atmospheric temperature structure and tropical lower stratospheric water vapour concentrations. For climate models, we demonstrate that these historically constrained relationships are highly predictive of the water vapour response to increased atmospheric carbon dioxide. We obtain an observationally constrained range for stratospheric water vapour changes per degree of global warming of 0.31 ± 0.39 ppmv K⁻¹. Across 61 climate models, we find that a large fraction of future model projections are inconsistent with observational evidence. In particular, frequently projected strong increases (>1 ppmv K⁻¹) are highly unlikely. Our constraint represents a 50% decrease in the 95th percentile of the climate model uncertainty distribution, which has implications for surface warming, ozone recovery and the tropospheric circulation response under climate change.