Many Himalayan glaciers are characterised in their lower reaches by a rock debris layer. This debris insulates the glacier surface from atmospheric warming and complicates the response to climate change compared to glaciers with clean-ice surfaces. Debris-covered glaciers can persist well below the altitude that would be sustainable for clean-ice glaciers, resulting in much longer timescales of mass loss and meltwater production. The properties and evolution of supraglacial debris present a considerable challenge to understanding future glacier change. Existing approaches to predicting variations in glacier volume and meltwater production rely on numerical models that represent the processes governing glaciers with clean-ice surfaces, and yield conflicting results. We developed a numerical model that couples the flow of ice and debris and includes important feedbacks between debris accumulation and glacier mass balance. To investigate the impact of debris transport on the response of a glacier to recent and future climate change, we applied this model to a large debris-covered Himalayan glacier-Khumbu Glacier in Nepal. Our results demonstrate that supraglacial debris prolongs the response of the glacier to warming and causes lowering of the glacier surface in situ, concealing the magnitude of mass loss when compared with estimates based on glacierised area. Since the Little Ice Age, Khumbu Glacier has lost 34% of its volume while its area has reduced by only 6%. We predict a decrease in glacier volume of 8-10% by AD2100, accompanied by dynamic and physical detachment of the debris-covered tongue from the active glacier within the next 150 yr. This detachment will accelerate rates of glacier decay, and similar changes are likely for other debris-covered glaciers in the Himalaya.