Aquatic non‐native invasive species are commonly traded in the worldwide water garden and aquarium markets, and some of these species pose major threats to the economy, the environment, and human health. Understanding the potential suitable habitat for these species at a global scale and at regional scales can inform risk assessments and predict future potential establishment. Typically, global habitat suitability models are fit for freshwater species with only climate variables, which provides little information about suitable terrestrial conditions for aquatic species. Remotely sensed data including topography and land cover data have the potential to improve our understanding of suitable habitat for aquatic species. In this study, we fit species distribution models using five different model algorithms for three non‐native aquatic invasive species with bioclimatic, topographic, and remotely sensed covariates to evaluate potential suitable habitat beyond simple climate matches. The species examined included a frog (Xenopus laevis), toad (Bombina orientalis), and snail (Pomacea spp.). Using a unique modeling approach for each species including background point selection based on known established populations resulted in robust ensemble habitat suitability models. All models for all species had test area under the receiver operating characteristic curve values greater than 0.70 and percent correctly classified values greater than 0.65. Importantly, we employed multivariate environmental similarity surface maps to evaluate potential extrapolation beyond observed conditions when applying models globally. These global models provide necessary forecasts of where these aquatic invasive species have the potential for establishment outside their native range, a key component in risk analyses.