By the end of this century, human-induced climate change and habitat loss may drastically reduce biodiversity, with expected effects on many amphibian lineages. One of these effects is the shift in the geographic distributions of species when tracking suitable climates. Here, we employ a macroecological approach to dynamically model geographic range shifts by coupling ecological niche models and eco-evolutionary mechanisms, aiming to assess the probability of evolutionary rescue (i.e., rapid adaptation) and dispersal under climate change. Evolutionary models estimated the probability of population persistence by adapting to changes in the temperature influenced by precipitation in the following decades, while compensating the fitness reduction and maintaining viable populations in the new climates. In addition, we evaluated emerging patterns of species richness and turnover at the assemblage level. Our approach was able to identify which amphibian populations among 7,193 species at the global scale could adapt to temperature changes or disperse into suitable regions in the future. Without evolutionary adaptation and dispersal, 47.7% of the species could go extinct until the year 2,100, whereas adding both processes will slightly decrease this extinction rate to 36.5%. Although adaptation to climate is possible for populations in about 25.7% of species, evolutionary rescue is the only possibility to avoid extinction in 4.2% of them. Dispersal will allow geographic range shifts for 49.7% of species, but only 6.5% may avoid extinction by reaching climatically suitable environments. This reconfiguration of species distributions and their persistence creates new assemblage-level patterns at the local scale. Temporal beta-diversity across the globe showed relatively low levels of species turnover, mainly due to the loss of species. Despite limitations with obtaining data, our approach provides more realistic assessments of species responses to ongoing climate changes. It shows that, although dispersal and evolutionary rescue may attenuate species losses, they are not enough to avoid a significant reduction of species’ geographic ranges in the future. Actions that guarantee a higher potential of adaptation (e.g., genetic diversity through larger population sizes) and increased connectivity for species dispersion to track suitable climates become essential, increasing the resilience of biodiversity to climate change.