Volcanic eruptions can impact the mass balance of ice sheets through changes in climate and the radiative properties of the ice. Yet, empirical evidence highlighting the sensitivity of ancient ice sheets to volcanism is scarce. Here we present an exceptionally well-dated annual glacial varve chronology recording the melting history of the Fennoscandian Ice Sheet at the end of the last deglaciation (similar to 13,200-12,000 years ago). Our data indicate that abrupt ice melting events coincide with volcanogenic aerosol emissions recorded in Greenland ice cores. We suggest that enhanced ice sheet runoff is primarily associated with albedo effects due to deposition of ash sourced from high-latitude volcanic eruptions. Climate and snow-pack mass-balance simulations show evidence for enhanced ice sheet runoff under volcanically forced conditions despite atmospheric cooling. The sensitivity of past ice sheets to volcanic ashfall highlights the need for an accurate coupling between atmosphere and ice sheet components in climate models.