Sub-Saharan West Africa is a vulnerable region where a better quantification and understanding of the impact of climate change on crop yields is urgently needed. Here, we have applied the process-based crop model SARRA-H calibrated and validated over multi-year field trials and surveys at eight contrasting sites in terms of climate and agricultural practices in Senegal, Mali, Burkina Faso and Niger. The model gives a reasonable correlation with observed yields of sorghum and millet under a range of cultivars and traditional crop management practices. We applied the model to more than 7000 simulations of yields of sorghum and millet for 35 stations across West Africa and under very different future climate conditions. We took into account 35 possible climate scenarios by combining precipitation anomalies from −20% to 20% and temperature anomalies from +0 to +6 • C. We found that most of the 35 scenarios (31/35) showed a negative impact on yields, up to −41% for +6 • C/ − 20% rainfall. Moreover, the potential future climate impacts on yields are very different from those recorded in the recent past. This is because of the increasingly adverse role of higher temperatures in reducing crop yields, irrespective of rainfall changes. When warming exceeds +2 • C, negative impacts caused by temperature rise cannot be counteracted by any rainfall change. The probability of a yield reduction appears to be greater in the Sudanian region (southern Senegal, Mali, Burkina Faso, northern Togo and Benin), because of an exacerbated sensitivity to temperature changes compared to the Sahelian region (Niger, Mali, northern parts of Senegal and Burkina Faso), where crop yields are more sensitive to rainfall change. Finally, our simulations show that the photoperiod-sensitive traditional cultivars of millet and sorghum used by local farmers for centuries seem more resilient to future climate conditions than modern cultivars bred for their high yield potential (−28% versus −40% for the +4 • C/ − 20% scenario). Photoperiod-sensitive cultivars counteract the effect of temperature increase on shortening cultivar duration and thus would likely avoid the need to shift to cultivars with a greater thermal time requirement. However, given the large difference in mean yields of the modern versus traditional varieties, the modern varieties would still yield more under optimal fertility conditions in a warmer world, even if they are more affected by climate change. S Online supplementary data available from stacks.iop.org/ERL/8/014040/mmedia Content from this work may be used under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.