AbstractGroundwater stored in weathered basement aquifers (WBAs) is a strategic water resource. In this study, we investigate the productivity of WBAs and sustainability of groundwater abstractions using a novel process‐based stochastic modeling approach, which is applied to simulate abstractions in the Precambrian basement aquifer in Ghana. The statistical distribution of the generated synthetic yield data was found in very good agreement with observed yield data from the same Ghanaian aquifer. Further analysis provided robust insights regarding how different hydrogeological parameters of the WBA, and their interplay, control aquifer productivity and sustainability. Results indicate that 97% of the simulated abstractions could sustain the yield of a hand pump (6 L/min), approximately 30% could also sustain yields >60 L/min, while only 1% could sustain yields greater than 300 L/min. The model indicates that an aquifer transmissivity value of approximately 1.4 m2/day is required for a successful hand‐pumped borehole, while a higher yielding source (60 L/min) requires a transmissivity value of at least 9.5 m2/day. A global sensitivity analysis of 13 model input parameters shows that the thickness of the regolith and the maximum hydraulic conductivity developed at the base of the saprolite are the critical factors controlling success and sustainability for low yielding hand‐pumped boreholes. For higher yielding supplies, the net recharge, the depth to groundwater, and the aquifer extent become increasingly significant. Results from this work have important implications for the potential for increased development of groundwater from WBAs in tropical Africa.