Uncertainty in the future evolution of tropical rainfall is linked to circulation changes under warming. In Africa, a key barrier to interpreting rainfall changes is our limited understanding of water vapor transport across the continent. Here, we show that a series of nocturnal easterly Low‐Level Jets (LLJs), which form in the valleys punctuating the East African rift system, transport the majority of water vapor to central Africa from the Indian Ocean. There is a robust connection between strengthened LLJs and drought in eastern and southern Africa at interannual timescales, mediated by an increase in low‐level divergence and water vapor export. Analysis of climate model simulations at a wide range of resolutions (250–4.5 km) suggests that grid lengths <60 km are needed to simulate the salient structures of LLJs. The failure of coarse resolution models to capture LLJs is linked with biases in rainfall climatology and variability across the continent.