In this paper, we investigate the long-term effects of climate change on the mobility of working-age people. We use a world economy model that covers almost all the countries around the world, and distinguishes between rural and urban regions as well as between flooded and unflooded areas. The model is calibrated to match international and internal mobility data by education level for the last 30 years, and is then simulated under climate change variants. We endogenize the size, dyadic, and skill structure of climate migration. When considering moderate climate scenarios, we predict mobility responses in the range of 70–108 million workers over the course of the twenty-first century. Most of these movements are local or inter-regional. South–South international migration responses are smaller, while the South–North migration response is of the “brain drain” type and induces a permanent increase in the number of foreigners in OECD countries in the range of 6–9% only. Changes in the sea level mainly translate into forced local movements. By contrast, inter-regional and international movements are sensitive to temperature-related changes in productivity. Lastly, we show that relaxing international migration restrictions may exacerbate the poverty effect of climate change at origin if policymakers are unable to select/screen individuals in extreme poverty.