The Amazon rainforest is disproportionately important for global carbon storage and biodiversity. The system couples the atmosphere and land, with moist forest that depends on convection to sustain gross primary productivity and growth. Earth system models that estimate future climate and vegetation show little agreement in Amazon simulations. Here we show that biases in internally generated climate, primarily precipitation, explain most of the uncertainty in Earth system model results; models, empirical data and theory converge when precipitation biases are accounted for. Gross primary productivity, above-ground biomass and tree cover align on a hydrological relationship with a breakpoint at ~2000 mm annual precipitation, where the system transitions between water and radiation limitation of evapotranspiration. The breakpoint appears to be fairly stable in the future, suggesting resilience of the Amazon to climate change. Changes in precipitation and land use are therefore more likely to govern biomass and vegetation structure in Amazonia.Earth system model simulations of future climate in the Amazon show little agreement. Here, the authors show that biases in internally generated climate explain most of this uncertainty and that the balance between water-saturated and water-limited evapotranspiration controls the Amazon resilience to climate change.