Reduced evaporation due to dry soils can affect the land surface energy balance, with implications for local and downwind precipitation. When evaporation is constrained by soil moisture, the atmospheric supply of water is depleted, and this deficit may propagate in time and space. This mechanism could theoretically result in the self-propagation of droughts, but the extent to which this process occurs is unknown. Here we isolate the influence of soil moisture drought on downwind precipitation using Lagrangian moisture tracking constrained by observations from the 40 largest recent droughts worldwide. We show that dryland droughts are particularly prone to self-propagating, because evaporation tends to respond strongly to enhanced soil water stress. In drylands precipitation can decline by more than 15% due to upwind drought in during a single event, and up to 30% during individual months. In light of projected widespread reductions in water availability, this feedback may further exacerbate future droughts.