Recent outbreaks of animal-borne emerging infectious diseases have likely been precipitated by a complex interplay of changing ecological, epidemiological and socio-economic factors. Here, we develop modelling methods that capture elements of each of these factors, to predict the risk of Ebola virus disease (EVD) across time and space. Our modelling results match previously-observed outbreak patterns with high accuracy, and suggest further outbreaks could occur across most of West and Central Africa. Trends in the underlying drivers of EVD risk suggest a 1.75 to 3.2-fold increase in the endemic rate of animal-human viral spill-overs in Africa by 2070, given current modes of healthcare intervention. Future global change scenarios with higher human population growth and lower rates of socio-economic development yield a fourfold higher likelihood of epidemics occurring as a result of spill-over events. Our modelling framework can be used to target interventions designed to reduce epidemic risk for many zoonotic diseases.