AimInvasive alien species (IAS) can cause profound impacts on ecosystem function and diversity, human health, well‐being and livelihoods. Climate change is an important driver of biological invasions, so it is critical to develop models and climate‐driven scenarios of IAS range shifts to establish preventive measures. In this study, we analyse how projected changes in the frequency and magnitude of climate extreme events could affect the spread of the six most widely distributed invasive vertebrate species in the Iberian Peninsula.LocationIberian Peninsula.TaxaRed avadavat (Amandava amandava), common waxbill (Estrilda astrild), monk parakeet (Myiopsitta monachus), rose‐ringed parakeet (Psittacula krameri), American mink (Neovison vison) and pond slider (Trachemys scripta).MethodsWe followed best‐practice standards for species distribution models (SDMs) regarding handling of the response and predictor variables, model building and evaluation using metrics that assess different facets of model performance. We used an ensemble approach with four modelling methods of varying complexity, including both regression‐based and tree‐based machine‐learning algorithms. We analysed five regional models for current (1971–2000) and future climate (2021–2050). We used principal components analysis to assess consensus among model outputs and positively weighed predictions from well‐performing models.ResultsSelected models showed high consensus and good predictive capacity on block cross‐validation areas. Generalized Linear Models and Generalized Additive Models scored highest in reliability (calibration), but Bayesian Additive Regression Trees provided the best balance between calibration and discrimination capacity. Forecasts include visible changes in environmental favourability, with losses generally outweighing the gains, but with some areas becoming more favourable for several species.Main conclusionsIncreased frequency and/or intensity of climate extreme events associated with ongoing climate change are projected to reduce overall invasion risk for the species examined although increases in favourability should be expected locally.