The NCEP/NCAR re-analyses as well as ensemble integrations with an atmospheric GCM indicate that interannual variations in Sahel rainfall are related to variations in the mean sea level pressure (MSLP) over the Sahara. In turn the MSLP variations are related to the global distribution of surface air temperature (SAT). An increase in SAT over the Sahara, relative to the surrounding oceans, decreases the MSLP over the Sahara, thereby increasing the Sahel rainfall. We hypothesize that through this mechanism greenhouse warming will cause an increase in Sahel rainfall, because the warming is expected to be more prominent over the summer continents than over the oceans. This has been confirmed using an ensemble of 62 coupled model runs forced with a business as usual scenario. The ensemble mean increase in Sahel rainfall between 1980 and 2080 is about 1--2 mm day-1 (25--50%) during July--September, thereby strongly reducing the probability of prolonged droughts.