Invasive species can alter the structure and function of the communities they invade, as well as lead to biotic homogenization across their invasive range, thus affecting large‐scale diversity patterns. The mechanisms by which invasive species can lead to biotic homogenization are poorly understood. We argue that invasive species acting as strong, deterministic, and consistent filters within and across invaded communities are likely to cause biotic homogenization at multiple spatial scales. We studied Bromus inermis Leyss. invasion into eight grasslands covering most of the grassland and parkland natural regions of Alberta (western Canada). Specifically, we tested whether B. inermis (1) has a strong impact on species richness and composition, (2) consistently alters resources (nutrients, light, and soil moisture), imposing the same ecological filter to species establishment and persistence across sites, and hence (3) whether it leads to biotic homogenization within and across sites. We recorded plant cover and resources across native‐to‐invaded transition areas combining space‐for‐time substitutions with time‐series data analyses. Bromus inermis invasion was associated with rapid biotic homogenization of communities, within and among the eight grasslands. The sharp changes in species relative abundances following invasion was the initial driver of biotic homogenization, and species loss was delayed. Supporting the idea that biotic homogenization can occur when an invasive species presents a broad and consistent filter, resources modified by B. inermis invasion (particularly light and certain nutrients) were altered rather consistently within and across sites. The 50% reduction in light was likely the initial driver of biotic homogenization, and the increase in nutrient availability probably facilitates the displacement of species from the invaded areas and could lead to the establishment of self‐reinforcing dynamics. Overall, our results support the idea that invaders acting as strong, deterministic, and consistent ecological filters are likely to cause biotic homogenization of the communities they invade.