Glacier mass loss is a key contributor to sea-level change1,2, slope instability in high-mountain regions3,4 and the changing seasonality and volume of river flow5–7. Understanding the causes, mechanisms and time scales of glacier change is therefore paramount to identifying successful strategies for mitigation and adaptation. Here, we use temperature and precipitation fields from the Coupled Model Intercomparison Project Phase 5 output to force a glacier evolution model, quantifying mass responses to future climatic change. We find that contemporary glacier mass is in disequilibrium with the current climate, and 36 ± 8% mass loss is already committed in response to past greenhouse gas emissions. Consequently, mitigating future emissions will have only very limited influence on glacier mass change in the twenty-first century. No significant differences between 1.5 and 2 K warming scenarios are detectable in the sea-level contribution of glaciers accumulated within the twenty-first century. In the long-term, however, mitigation will exert strong control, suggesting that ambitious measures are necessary for the long-term preservation of glaciers.