Africa’s central Sahel region has experienced prolonged drought conditions in the past, while rainfall has recovered more recently. Global climate models project anything from no change to a strong wetting trend under unabated climate change; and they have difficulty reproducing the complex historical record. Here we show that when a period of dominant aerosol forcing is excluded, a consistent wetting response to greenhouse-gas induced warming emerges in observed rainfall. Using the observed response coefficient estimate as a constraint, we find that CMIP6 climate models with a realistic past rainfall response show a smaller spread, and higher median, of projected future rainfall change, compared to the full ensemble. In particular, very small or negative rainfall trends are absent from the constrained ensemble. Our results provide further evidence for a robust Sahel rainfall increase in response to greenhouse-gas forcing, consistent with recent observations, and including the possibility of a very strong increase.