Climate change and biological invasions are primary threats to global biodiversity that may interact in the future. To date, the hypothesis that climate change will favour non‐native species has been examined exclusively through local comparisons of single or few species. Here, we take a meta‐analytical approach to broadly evaluate whether non‐native species are poised to respond more positively than native species to future climatic conditions. We compiled a database of studies in aquatic and terrestrial ecosystems that reported performance measures of non‐native (157 species) and co‐occurring native species (204 species) under different temperature, CO2 and precipitation conditions. Our analyses revealed that in terrestrial (primarily plant) systems, native and non‐native species responded similarly to environmental changes. By contrast, in aquatic (primarily animal) systems, increases in temperature and CO2 largely inhibited native species. There was a general trend towards stronger responses among non‐native species, including enhanced positive responses to more favourable conditions and stronger negative responses to less favourable conditions. As climate change proceeds, aquatic systems may be particularly vulnerable to invasion. Across systems, there could be a higher risk of invasion at sites becoming more climatically hospitable, whereas sites shifting towards harsher conditions may become more resistant to invasions.