Non-indigenous species (NIS) pose a major threat to biodiversity and the functioning and services of ecosystems. Despite their rapid spread in coastal waters worldwide, biotic invasions are widely disregarded in marine conservation planning. To guide conservation actions, a better understanding of the underlying mechanisms determining the success of NIS are therefore needed. Here we develop a joint modelling approach to identify the key drivers and community assembly processes determining the occurrence of invasive benthic invertebrates, using Danish coastal waters as a case study. To reflect factors affecting the introduction, establishment and spread of NIS throughout the area, we compiled long-term monitoring data on NIS, as well as information on commercial shipping, environmental conditions and estimates of larvae settling densities derived from drift model simulations informed by species traits. We then applied a set of species distribution models to identify the key drivers determining the occurrence of NIS. Our results demonstrate a significant positive effect of vessel activity, a negative effect of depth and bottom salinity, as well as a positive effect of the simulated settling densities on the probability of presence. Taken together, our results highlight the role of commercial shipping, habitat characteristics and passive advection of early-life stages on the success of NIS. Our joint modelling approach provide improved process understanding on the key community assembly processes determining the presence of NIS and may serve to guide monitoring, management and conservation planning in order to limit future invasions and their negative consequences on coastal ecosystems.