Outbreaks of Rift Valley fever (RVF), a relatively recently emerged zoonosis endemic to large parts of sub-Saharan Africa that has the potential to spread beyond the continent, have profound health and socio-economic impacts, particularly in communities where resilience is already low. Here output from a new, dynamic disease model [the Liverpool RVF (LRVF) model], driven by downscaled, bias-corrected climate change data from an ensemble of global circulation models from the Inter-Sectoral Impact Model Intercomparison Project run according to two radiative forcing scenarios [representative concentration pathway (RCP)4.5 and RCP8.5], is combined with results of a spatial assessment of social vulnerability to the disease in eastern Africa. The combined approach allowed for analyses of spatial and temporal variations in the risk of RVF to the end of the current century. Results for both scenarios highlight the high-risk of future RVF outbreaks, including in parts of eastern Africa to date unaffected by the disease. The results also highlight the risk of spread from/to countries adjacent to the study area, and possibly farther afield, and the value of considering the geography of future projections of disease risk. Based on the results, there is a clear need to remain vigilant and to invest not only in surveillance and early warning systems, but also in addressing the socio-economic factors that underpin social vulnerability in order to mitigate, effectively, future impacts.