Abstract Understanding the factors responsible for the success of exotic species is a prevalent issue in invasion biology. Although the ecological traits of exotic species are known to play a major role, it is still unknown which traits are responsible for the different dimensions of invasiveness among vertebrates. Here, we assessed the ecological, morphological and behavioural profile of 222 exotic freshwater fish along different levels of establishment, defined by the number of basins in which the exotic species are established and the location of establishment. Using a trait‐based multidimensional space complemented by a trait‐by‐trait analysis, we attempted to classified exotic vertebrates given their intrinsic traits across establishment levels ranging from species with low establishment to super‐established species. We found that fish with low establishment were clustered in the trait space, showing similar traits characterized by low‐temperature amplitude, no parental care and zoobenthic diet. By contrast, super‐established fish had a broader range of functional strategies, with a high proportion of species having multiple diets and a high level of parental care. Overall, fish with low establishment had low functional overlap with other fish at higher levels of establishment. Our findings highlight the importance of considering trait variability in the species' level of establishment to more accurately anticipate their ability to establish and spread. Read the free Plain Language Summary for this article on the Journal blog.