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The observed temperature increase due to anthropogenic carbon emissions has impacted economies worldwide. National income levels in origin and destination countries influence international migration. Emigration is relatively low not only from high income countries but also from very poor regions, which is explained in current migration theory by credit constraints and lower average education levels, among other reasons. These relationships suggest a potential non-linear, indirect effect of climate change on migration through this indirect channel. Here we explore this effect through a counterfactual analysis using observational data and a simple model of migration. We show that a world without climate change would have seen less migration during the past 30 years, but that this effect is strongly reduced due to inhibited mobility. Our framework suggests that migration within the Global South has been strongly reduced because these countries have seen less economic growth than they would have experienced without climate change. Importantly, climate change has impacted international migration in the richer and poorer parts of the world very differently. In the future, climate change may keep increasing global migration as it slows down countries' transition across the middle-income range associated with the highest emigration rates.