The insurance hypothesis, stating that biodiversity can increase ecosystem stability, has received wide research and political attention. Recent experiments suggest that climate change can impact how plant diversity influences ecosystem stability, but most evidence of the biodiversity-stability relationship obtained to date comes from local studies performed under a limited set of climatic conditions. Here, we investigate how climate mediates the relationships between plant (taxonomical and functional) diversity and ecosystem stability across the globe. To do so, we coupled 14 years of temporal remote sensing measurements of plant biomass with field surveys of diversity in 123 dryland ecosystems from all continents except Antarctica. Across a wide range of climatic and soil conditions, plant species pools, and locations, we were able to explain 73% of variation in ecosystem stability, measured as the ratio of the temporal mean biomass to the SD. The positive role of plant diversity on ecosystem stability was as important as that of climatic and soil factors. However, we also found a strong climate dependency of the biodiversity-ecosystem stability relationship across our global aridity gradient. Our findings suggest that the diversity of leaf traits may drive ecosystem stability at low aridity levels, whereas species richness may have a greater stabilizing role under the most arid conditions evaluated. Our study highlights that to minimize variations in the temporal delivery of ecosystem services related to plant biomass, functional and taxonomic plant diversity should be particularly promoted under low and high aridity conditions, respectively.