Climate change is expected to negatively impact cocoa production in West and Central Africa, where over 70 % of cocoa is grown. However, effects of temperature, precipitation and atmospheric carbon dioxide concentration [CO2] on cocoa tree physiology and productivity are poorly understood. Consequently, climate-change implications have not been adequately considered. The objective was to improve understanding of potential cocoa productivity responses to climate change by mid-century (2060). Using a crop model, we simulated potential water-limited cocoa yields (Yw) to evaluate effects of warming and precipitation changes based on five plausible general circulation models (GCMs) climate-change scenarios, with and without elevated CO2. We examined how variation in Yw was associated with that of climate using mixed-effects models and estimated total cocoa production on current plantation area under current low-input and high-input scenarios. With notable exceptions, by mid-century, Yw and suitable area were projected to increase, particularly when assuming full elevated [CO2] effects and under wetter climate-change scenarios. We identified a (south) east - west gradient with higher yield increases (∼39–60 %) in Cameroon and Nigeria compared to Ghana and Côte d'Ivoire (∼30–45 %). Larger yield reductions (∼12 %) were identified in Côte d'Ivoire and Ghana than in Nigeria (∼10 %) and Cameroon (∼2 %). Additionally, gains in suitable area were projected for Nigeria (∼17–20 Mha), Cameroon (∼11–12 Mha), and Ghana (∼2 Mha) while Côte d'Ivoire could lose ∼6–11 Mha (i.e., ∼27–50 % of current suitable area). Inter-annual yield variability was higher in areas with low yields. Based on the mid climate-change scenario, country-level production on current plantation area in Côte d'Ivoire and Ghana could be maintained. Projected increases and shorter length in dry season precipitation strongly determined increases in Yw and reductions in Yw variability, respectively. Thus, despite projected warming and precipitation changes, many current cocoa-growing areas may maintain or increase their productivity, particularly if full effects of elevated [CO2] are assumed.