The reliability of transferring species distribution models (SDMs) to new ranges and future climates has been widely debated. Biological invasions offer the unique opportunity to evaluate model transferability, as distribution data between species' native and introduced ranges are geographically independent of each other. Here, we performed the first global quantitative synthesis of the spatial transferability of SDMs for 235 invasive species and assessed the association of model transferability with the focal invader, model choice and parameterisation. We found that SDMs had limited spatial transferability overall. However, model transferability was higher for terrestrial endotherms, species introduced from or to the Southern Hemisphere, and species introduced more recently. Model transferability was also positively associated with the number of presences for model calibration and evaluation, respectively, but negatively with the number of predictors. These findings highlight the importance of considering the characteristics of the focal invader, environment and modelling in the application and assessment of SDMs.