The landscape shrouded by Antarctica’s ice sheet provides important insights into its history and influences the ice response to climate forcing, yet much of this critical basal boundary remains poorly understood. With ice-penetrating-radar technology yet to be developed to sound the bed of the Antarctic Ice Sheet from space, our understanding of the subglacial landscape has depended upon interpolation between irregularly distributed geophysical surveys. Despite increasing geophysical coverage and sophisticated developments in spatial interpolation, this has led to significant spatial biases in maps of Antarctica’s subglacial landscape. Recently-acquired, high-resolution maps of the ice surface now offer a transformative basis for recovering subglacial topography. We present a new map of Antarctica’s subglacial topography produced by an inversion technique that leverages the principle that stress changes associated with ice flow over bedrock obstacles produce ice-surface topography. Our results significantly enrich our understanding of mesoscale (10s of km width) landforms beneath the Antarctic Ice Sheet, revealing many new features and accentuating knowledge of subglacial mountain ranges and basins. The new map unmasks the true continent-wide spatial distribution of Antarctica’s subglacial roughness and geomorphology, outlines a pathway towards more accurate interpolation of poorly surveyed areas, and guides future targeted geophysical surveying.