The effects of precipitation changes on tropical East African ecosystems and human populations is poorly understood due to the complex interplay between global and regional processes and missing data from key regions and time periods. We generate a water-budget model for Lake Victoria, the largest tropical lake in the world, the source of the White Nile, and a region that supports some of the densest human populations in Africa, that assesses the impact of changing climate on lake levels and the rate of lake level change. Model results demonstrate that significant changes in the size and volume of Lake Victoria are possible in response to changes in temperature, precipitation, and orbital forcing. This modeling indicates that Lake Victoria can transition back and forth between modern lake levels and complete desiccation in centuries to a few millennia, which is rapid enough to allow for two previously observed desiccation events between 14-18 ka, during which time the lake drained and refilled twice. Combined observations from modeling and estimates of paleoprecipitation indicate that Lake Victoria was likely desiccated between 94-36 ka. This dry interval partially overlaps the megadrought (140-70 ka) identified in Lakes Malawi and Tanganyika further south, and the cooler, drier conditions identified in the Gulf of Aden between 75-50 ka. This prolonged desiccation was probably driven by eccentricity-enhanced precession and high-latitude forcing that affected the Congo Air Boundary convergence. Using future climate projections, our model also predicts that at current rates of temperature change and previous rates of lake level fall, Lake Victoria could have no outlet to the White Nile within 10 years, and Kenya could lose access to the lake in <400 years, which would significantly affect the economic resources supplied by Lake Victoria to the East African Community.