Aim Climate variability threatens to destabilize production in many ecosystems. Asynchronous species dynamics may buffer against such variability when a decrease in performance by some species is offset by an increase in performance of others. However, high climatic variability can eliminate species through stochastic extinctions or cause similar stress responses among species that reduce buffering. Local conditions, such as soil nutrients, can also alter production stability directly or by influencing asynchrony. We test these hypotheses using a globally distributed sampling experiment. Location Grasslands in North America, Europe and Australia. Time period Annual surveys over 5 year intervals occurring between 2007 and 2014. Major taxa studied Herbaceous plants. Methods We sampled annually the per species cover and aboveground community biomass [net primary productivity (NPP)], plus soil chemical properties, in 29 grasslands. We tested how soil conditions, combined with variability in precipitation and temperature, affect species richness, asynchrony and temporal stability of primary productivity. We used bivariate relationships and structural equation modelling to examine proximate and ultimate relationships. Results Climate variability strongly predicted asynchrony, whereas NPP stability was more related to soil conditions. Species richness was structured by both climate variability and soils and, in turn, increased asynchrony. Variability in temperature and precipitation caused a unimodal asynchrony response, with asynchrony being lowest at low and high climate variability. Climate impacted stability indirectly, through its effect on asynchrony, with stability increasing at higher asynchrony owing to lower inter‐annual variability in NPP. Soil conditions had no detectable effect on asynchrony but increased stability by increasing the mean NPP, especially when soil organic matter was high. Main conclusions We found globally consistent evidence that climate modulates species asynchrony but that the direct effect on stability is low relative to local soil conditions. Nonetheless, our observed unimodal responses to variability in temperature and precipitation suggest asynchrony thresholds, beyond which there are detectable destabilizing impacts of climate on primary productivity.