Antarctica's continental-scale ice sheets have evolved over the past 50 million years. However, the dearth of ice-proximal geological records limits our understanding of past East Antarctic Ice Sheet (EAIS) behaviour and thus our ability to evaluate its response to ongoing environmental change. The EAIS is marine-terminating and grounded below sea level within the Aurora subglacial basin, indicating that this catchment, which drains ice to the Sabrina Coast, may be sensitive to climate perturbations. Here we show, using marine geological and geophysical data from the continental shelf seaward of the Aurora subglacial basin, that marine-terminating glaciers existed at the Sabrina Coast by the early to middle Eocene epoch. This finding implies the existence of substantial ice volume in the Aurora subglacial basin before continental-scale ice sheets were established about 34 million years ago. Subsequently, ice advanced across and retreated from the Sabrina Coast continental shelf at least 11 times during the Oligocene and Miocene epochs. Tunnel valleys associated with half of these glaciations indicate that a surface-meltwater-rich sub-polar glacial system existed under climate conditions similar to those anticipated with continued anthropogenic warming. Cooling since the late Miocene resulted in an expanded polar EAIS and a limited glacial response to Pliocene warmth in the Aurora subglacial basin catchment. Geological records from the Sabrina Coast shelf indicate that, in addition to ocean temperature, atmospheric temperature and surface-derived meltwater influenced East Antarctic ice mass balance under warmer-than-present climate conditions. Our results imply a dynamic EAIS response with continued anthropogenic warming and suggest that the EAIS contribution to future global sea-level projections may be under-estimated.