The century-long debate over the origins of inner gorges that were repeatedly covered by Quaternary glaciers hinges upon whether the gorges are fluvial forms eroded by subaerial rivers, or subglacial forms cut beneath ice. Here we apply cosmogenic nuclide exposure dating to seven inner gorges along ~500 km of the former Fennoscandian ice sheet margin in combination with a new deglaciation map. We show that the timing of exposure matches the advent of ice-free conditions, strongly suggesting that gorges were cut by channelized subglacial meltwater while simultaneously being shielded from cosmic rays by overlying ice. Given the exceptional hydraulic efficiency required for meltwater channels to erode bedrock and evacuate debris, we deduce that inner gorges are the product of ice sheets undergoing intense surface melting. The lack of postglacial river erosion in our seven gorges implicates subglacial meltwater as a key driver of valley deepening on the Baltic Shield over multiple glacial cycles.