The accelerating rate of change in biodiversity patterns, mediated by ever increasing human pressures and global warming, demands a better understanding of the relationship between the structure of biological communities and ecosystem functioning (BEF). Recent investigations suggest that the functional structure of communities, i.e. the composition and diversity of functional traits, is the main driver of ecological processes. However, the predictive power of BEF research is still low, the integration of all components of functional community structure as predictors is still lacking, and the multifunctionality of ecosystems (i.e. rates of multiple processes) must be considered. Here, using a multiple-processes framework from grassland biodiversity experiments, we show that functional identity of species and functional divergence among species, rather than species diversity per se, together promote the level of ecosystem multifunctionality with a predictive power of 80%. Our results suggest that primary productivity and decomposition rates, two key ecosystem processes upon which the global carbon cycle depends, are primarily sustained by specialist species, i.e. those that hold specialized combinations of traits and perform particular functions. Contrary to studies focusing on single ecosystem functions and considering species richness as the sole measure of biodiversity, we found a linear and non-saturating effect of the functional structure of communities on ecosystem multifunctionality. Thus, sustaining multiple ecological processes would require focusing on trait dominance and on the degree of community specialization, even in species-rich assemblages.