Vegetation growth is affected not only by the concurrent climate, but also its status in the past and the associated lagged responses. Favorable climate in the past may stimulate vegetation growth to surpass the ecosystem carrying capacity, leave an ecosystem vulnerable to climate stresses. This phenomenon, known as structural overshoot, can greatly 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. When applied to satellite observation of terrestrial vegetation during 1981-2015, we find that structural overshoot contributed to 33.9% of the drought. Overshoot droughts occur more frequently in mid-latitude semi-arid or dry sub-humid regions, with higher impacts in boreal ecosystems. The fraction of droughts related to overshoot is strongly associated with biodiversity, with mean annual temperature, vegetation coverage, and aridity as secondary factors. These overshoot droughts are not only more likely to happen in warmer months, leading to higher risks of compound extreme drought and heat, but also causing faster vegetation decline compared to normal droughts, contributing to the development of flash drought, and causing large impact on ecosystem stability. Although the overall overshoot numbers have decreased over the past 35 years, the hotspots regions still exist, especially in vulnerable ecosystems where drought has become more prevalent.