Climate change affects the spatial and temporal distribution of crop yields, which can critically impair food security across scales. A number of previous studies have assessed the impact of climate change on mean crop yield and future food availability, but much less is known about potential future changes in interannual yield variability. Here, we evaluate future changes in relative interannual global wheat yield variability (the coefficient of variation (CV)) at 0.25° spatial resolution for two representative concentration pathways (RCP4.5 and RCP8.5). A multi-model ensemble of crop model emulators based on global process-based models is used to evaluate responses to changes in temperature, precipitation, and CO2. The results indicate that over 60% of harvested areas could experience significant changes in interannual yield variability under a high-emission scenario by the end of the 21st century (2066–2095). About 31% and 44% of harvested areas are projected to undergo significant reductions of relative yield variability under RCP4.5 and RCP8.5, respectively. In turn, wheat yield is projected to become more unstable across 23% (RCP4.5) and 18% (RCP8.5) of global harvested areas—mostly in hot or low fertilizer input regions, including some of the major breadbasket countries. The major driver of increasing yield CV change is the increase in yield standard deviation, whereas declining yield CV is mostly caused by stronger increases in mean yield than in the standard deviation. Changes in temperature are the dominant cause of change in wheat yield CVs, having a greater influence than changes in precipitation in 53% and 72% of global harvested areas by the end of the century under RCP4.5 and RCP8.5, respectively. This research highlights the potential challenges posed by increased yield variability and the need for tailored regional adaptation strategies.