The natural composition of terrestrial ecosystems can be shaped by climate to take advantage of local environmental conditions. Ecosystem functioning (e.g., interaction between photosynthesis and temperature) can also acclimate to different climatological states. The combination of these two factors thus determines ecological–climate interactions. A global empirical map of the sensitivity of vegetation to climate is derived using the response of satellite-observed greenness to interannual variations in temperature and precipitation. Mechanisms constraining ecosystem functioning are inferred by analyzing how the sensitivity of vegetation to climate varies across climate space. Analysis yields empirical evidence for multiple physical and biological mediators of the sensitivity of vegetation to climate at large spatial scales. In hot and wet locations, vegetation is greener in warmer years despite temperatures likely exceeding thermally optimum conditions. However, sunlight generally increases during warmer years, suggesting that the increased stress from higher atmospheric water demand is offset by higher rates of photosynthesis. The sensitivity of vegetation transitions in sign (greener when warmer or drier to greener when cooler or wetter) along an emergent line in climate space with a slope of about 59 mm yr⁻¹ °C⁻¹, twice as steep as contours of aridity. The mismatch between these slopes is evidence at a global scale of the limitation of both water supply due to inefficiencies in plant access to rainfall and plant physiological responses to atmospheric water demand. This empirical pattern can provide a functional constraint for process-based models, helping to improve predictions of the global-scale response of vegetation to a changing climate.