Since the 19th century, the addax (Addax nasomaculatus) has lost approximately 99% of its former range. Along with its close relatives, the blue antelope (Hippotragus leucophaeus) and the scimitar-horned oryx (Oryx dammah), the addax may be the third large African mammal species to go extinct in the wild in recent times. Despite this, the evolutionary history of this critically endangered species remains virtually unknown. To gain insight into the population history of the addax, we used hybridization capture to generate ten complete mitochondrial genomes from historical samples and assembled a nuclear genome. We found that both mitochondrial and nuclear diversity are low compared to other African bovids. Analysis of mitochondrial genomes revealed a most recent common ancestor ~32 kya (95% CI 11–58 kya) and weak phylogeographic structure, indicating that the addax likely existed as a highly mobile, panmictic population across its Sahelo–Saharan range in the past. PSMC analysis revealed a continuous decline in effective population size since ~2 Ma, with short intermediate increases at ~500 and ~44 kya. Our results suggest that the addax went through a major bottleneck in the Late Pleistocene, remaining at low population size prior to the human disturbances of the last few centuries.