The Anthropocene period is characterised by a general demographic shift from rural communities to urban centres that transform the predominantly wild global landscape into mostly cultivated land and cities. In addition to climate change, there are increased uncertainties in the water balance and these feedbacks cannot be modelled accurately due to scarce or incomplete in situ data. In African catchments with limited current and historical climate data, precise modelling of potential runoff regimes is difficult, but a growing number of model applications indicate that useful simulations are feasible. In this study, we used the new generation of soil and water assessment tool (SWAT) dubbed SWAT+ to assess the viability of using high resolution gridded data as an alternative to station observations to investigate surface runoff response to continuous land use change and future climate change. Simultaneously, under two representative concentration pathways (RCP4.5 and RCP8.5), six regional climate models (RCMs) from the Coordinated Regional Climate Downscaling Experiment Program (CORDEX) and their ensemble were evaluated for model skill and systematic biases and the best performing model was selected. The gridded data predicted streamflow accurately with a Nash–Sutcliffe efficiency greater than 0.89 in both calibration and validation phases. The analysis results show that further conversion of grasslands and forests to agriculture and urban areas doubled the runoff depth between 1984 and 2016. Climate projections predict a decline in March–May rainfall and an increase in the October–December season. Mean temperatures are expected to rise by about 1.3–1.5 °C under RCP4.5 and about 2.6–3.5 °C under RCP8.5 by 2100. Compared to the 2010–2016 period, simulated surface runoff response to climate change showed a decline under RCP4.5 and an increase under RCP8.5. In contrast, the combine effects of land use change and climate change simulated a steady increase in surface runoff under both scenarios. This suggests that the land use influence on the surface runoff response is more significant than that of climate change. The study results highlight the reliability of gridded data as an alternative to instrumental measurements in limited or missing data cases. More weight should be given to improving land management practices to counter the imminent increase in the surface runoff to avoid an increase in non-point source pollution, erosion, and flooding in the urban watersheds.