Global spread of non‐native species profoundly changed the world biodiversity patterns, but how it translates into functional changes remains unanswered at the world scale. We here show that while in two centuries the number of fish species per river increased on average by 15% in 1569 basins worldwide, the diversity of their functional attributes (i.e. functional richness) increased on average by 150%. The inflation of functional richness was paired with changes in the functional structure of assemblages, with shifts of species position toward the border of the functional space of assemblages (i.e. increased functional divergence). Non‐native species moreover caused shifts in functional identity toward higher body sized and less elongated species for most of assemblages throughout the world. Although varying between rivers and biogeographic realms, such changes in the different facets of functional diversity might still increase in the future through increasing species invasion and may further modify ecosystem functioning.