Uncertainties surrounding tree carbon allocation to growth are a major limitation to projections of forest carbon sequestration and response to climate change. The prevalence and extent to which carbon assimilation (source) or cambial activity (sink) mediate wood production are fundamentally important and remain elusive. We quantified source-sink relations across biomes by combining eddy-covariance gross primary production with extensive on-site and regional tree ring observations. We found widespread temporal decoupling between carbon assimilation and tree growth, underpinned by contrasting climatic sensitivities of these two processes. Substantial differences in assimilation-growth decoupling between angiosperms and gymnosperms were determined, as well as stronger decoupling with canopy closure, aridity, and decreasing temperatures. Our results reveal pervasive sink control over tree growth that is likely to be increasingly prominent under global climate change.