Abstract Invasive alien species and climate change are two of the most serious global environmental threats. In particular, it is of great interest to understand how changing climates could impact the distribution of invaders that pose serious threats to ecosystems and human activities. In this study, we developed ensemble species distribution models for predicting the current and future global distribution of the signal crayfish Pacifastacus leniusculus and the red swamp crayfish Procambarus clarkii, two of the most highly problematic invaders of freshwater ecosystems worldwide. We collected occurrence records of the species, from native and alien established ranges worldwide. These records in combination with averaged observations of current climatic conditions were used to calibrate a set of 10 distinct correlative models for estimating the climatic niche of each species. We next projected the estimated niches into the geographical space for the current climate conditions and for the 2050s and 2070s under representative concentration pathway 2.6 and 8.5 scenarios. Our species distribution models had high predictive abilities and suggest that annual mean temperature is the main driver of the distribution of both species. Model predictions indicated that the two crayfish species have not fully occupied their suitable climates and will respond differently to future climate scenarios in different geographic regions. Suitable climate for P. leniusculus was predicted to shift poleward and to increase in extent in North America and Europe but decrease in Asia. Regions with suitable climate for P. clarkii are predicted to widen in Europe but contract in North America and Asia. This study highlights that invasive species with different thermal preference are likely to respond differently to future climate changes. Our results provide important information for policy makers to design and implement anticipated measures for the prevention and control of these two problematic species.