Vegetation dynamics are affected not only by the concurrent climate but also by memory-induced lagged responses. For example, favourable climate in the past could stimulate vegetation growth to surpass the ecosystem carrying capacity, leaving an ecosystem vulnerable to climate stresses. This phenomenon, known as structural overshoot, could potentially contribute to worldwide drought stress and forest mortality but the magnitude of the impact is poorly known due to the dynamic nature of overshoot and complex influencing timescales. Here, we use a dynamic statistical learning approach to identify and characterize ecosystem structural overshoot globally and quantify the associated drought impacts. We find that structural overshoot contributed to around 11% of drought events during 1981–2015 and is often associated with compound extreme drought and heat, causing faster vegetation declines and greater drought impacts compared to non-overshoot related droughts. The fraction of droughts related to overshoot is strongly related to mean annual temperature, with biodiversity, aridity and land cover as secondary factors. These results highlight the large role vegetation dynamics play in drought development and suggest that soil water depletion due to warming-induced future increases in vegetation could cause more frequent and stronger overshoot droughts.