The 2013–2016 epidemic of Ebola virus disease was of unprecedented magnitude, duration and impact. Analysing 1610 Ebola virus genomes, representing over 5% of known cases, we reconstruct the dispersal, proliferation and decline of Ebola virus throughout the region. We test the association of geography, climate and demography with viral movement among administrative regions, inferring a classic ‘gravity’ model, with intense dispersal between larger and closer populations. Despite attenuation of international dispersal after border closures, cross-border transmission had already set the seeds for an international epidemic, rendering these measures ineffective in curbing the epidemic. We address why the epidemic did not spread into neighbouring countries, showing they were susceptible to significant outbreaks but at lower risk of introductions. Finally, we reveal this large epidemic to be a heterogeneous and spatially dissociated collection of transmission clusters of varying size, duration and connectivity. These insights will help inform interventions in future epidemics.