Our understanding of the community assembly processes acting on non-indigenous species (NIS), as well as the relationship with native species is limited, especially in marine ecosystems. To overcome this knowledge gap we here develop a trait-based approach based on the functional distinctiveness metric to assess niche overlap between NIS and native species, using high-resolution data on benthic invertebrate communities in the Baltic Sea. Our results show that NIS retain a certain degree of similarity with native species, but display one or a few singular traits (e.g., size, life span or bioturbation ability). Furthermore, we demonstrate that community assembly processes, including both environmental filtering and limiting similarity affect NIS establishment, but that their effects may be highly context dependent, as illustrated by pronounced spatial patterns in distinctiveness. Finally, our trait-based approach provides a generic framework applicable to other areas and organisms, to better understand and address biological invasions.