Aim Functional diversity encapsulates whole‐community responses to environmental gradients mediated by species traits. Under trait convergence, similar responses may cause distantly related taxa to exhibit spatially correlated functional diversity. We investigated whether similar responses of reef fish, coral and algal functional richness and disparity to the environment produce spatially correlated functional diversity patterns. Location Brazilian marine biogeographical province. Taxon Reef fish, corals, algae. Methods We analysed data from 40 coastal and oceanic sites distributed across 27 degrees of latitude in the Brazilian province. Using traits, we measured functional richness (FRic) and disparity (Rao's Q) and calculated Pearson's correlation (ρobs) between pairs of metrics and taxa. We used Bayesian multivariate linear models to model taxa functional richness and disparity relative to sea surface temperature (SST), turbidity, salinity, species richness and region, and to estimate the residual correlation (ρres) between metrics after accounting for these variables. Results The best fitted model contained SST, species richness and region, and explained about 56% of the variation in FRic and Rao's Q across taxa. Yet, FRic and Rao's Q of fish, algae and corals responded differently to environmental variables. Functional diversity metrics were less correlated between algae and corals than compared to fish. Observed correlations of FRic and Rao's Q were low to intermediate across taxa (average ρobs = 0.14), and residual correlations were even lower (average ρres = 0.02). Main conclusions SST, species richness and region had a widespread role in determining spatially congruent functional diversity offish, algae and corals across Brazilian reefs, despite their fundamentally different evolutionary histories. Low residual spatial correlations suggest that other mechanisms might also contribute to functional diversity patterns of reef taxa independently. Given the role of SST, species richness and region, the functional structure of these reefs might be compromised by climate change, pollution and overfishing.