Ecosystem processes are driven by both environmental variables and the attributes of component species. The extent to which these effects are independent and/or dependent upon each other has remained unclear. We assess the extent to which climate affects net primary productivity (NPP) both directly and indirectly via its effect on plant size and leaf functional traits. Using species occurrences and functional trait databases for North and South America, we describe the upper limit of woody plant height within 200 × 200 km grid-cells. In addition to maximum tree height, we quantify grid-cell means of three leaf traits (specific leaf area, and leaf nitrogen and phosphorus concentration) also hypothesized to influence productivity. Using structural equation modelling, we test the direct and indirect effects of environment and plant traits on remotely sensed MODIS-derived estimates of NPP, using plant size (satellite-measured canopy height and potential maximum tree height), leaf traits, growing season length, soil nutrients, climate and disturbances as explanatory variables. Our results show that climate affects NPP directly as well as indirectly via plant size in both tropical and temperate forests. In tropical forests NPP further increases with leaf phosphorus concentration, whereas in temperate forests it increases with leaf nitrogen concentration. In boreal forests, NPP most strongly increases with increasing temperature and neither plant size nor leaf traits have a significant influence. Synthesis. Our results suggest that at large spatial scales plant size and leaf nutrient traits can improve predictions of forest productivity over those based on climate alone. However, at higher latitudes their role is overridden by stressful climate. Our results provide independent empirical evidence for where and how global vegetation models predicting carbon fluxes could benefit from including effects of plant size and leaf stoichiometry.