The rate of biological invasions has strongly increased during the last decades, mostly due to the accelerated spread of species by increasing global trade and transport. Here, we combine the network of global cargo ship movements with port environmental conditions and biogeography to quantify the probability of new primary invasions through the release of ballast water. We find that invasion risks vary widely between coastal ecosystems and classify marine ecoregions according to their total invasion risk and the diversity of their invasion sources. Thereby, we identify high‐risk invasion routes, hot spots of bioinvasion and major source regions from which bioinvasion is likely to occur. Our predictions agree with observations in the field and reveal that the invasion probability is highest for intermediate geographic distances between donor and recipient ports. Our findings suggest that network‐based invasion models may serve as a basis for the development of effective, targeted bioinvasion management strategies.