Transportation networks play a crucial role for the spread of invasive species. Here, we combine the network of world-wide cargo ship movements with environmental conditions and biogeography, to develop a model for marine bioinvasion. We classify marine ecoregions according to their total invasion risk and the diversity of their invasion sources. Our predictions agree with observations in the field and reveal that invasion risks are highest for intermediate geographic distances. Our findings suggest that network-based invasion models facilitate the development of targeted mitigation strategies.