Global warming drives changes in Earth’s cloud cover, which, in turn, may amplify or dampen climate change. This “cloud feedback” is the single most important cause of uncertainty in Equilibrium Climate Sensitivity (ECS)—the equilibrium global warming following a doubling of atmospheric carbon dioxide. Using data from Earth observations and climate model simulations, we here develop a statistical learning analysis of how clouds respond to changes in the environment. We show that global cloud feedback is dominated by the sensitivity of clouds to surface temperature and tropospheric stability. Considering changes in just these two factors, we are able to constrain global cloud feedback to 0.43 ± 0.35 W⋅m<jats:sup>−2</jats:sup>⋅K<jats:sup>−1</jats:sup> (90% confidence), implying a robustly amplifying effect of clouds on global warming and only a 0.5% chance of ECS below 2 K. We thus anticipate that our approach will enable tighter constraints on climate change projections, including its manifold socioeconomic and ecological impacts.