Ice-sheet behaviour is disproportionately controlled by the dynamics of outlet glaciers that terminate in the ocean^{1, 2}. However, outlet-glacier dynamics—particularly over timescales longer than the observational record—are not well understood³, leading to uncertainties in our models of ice-sheet response to climate change. Here we use ¹⁰Be exposure ages and radiocarbon dating from the Sam Ford Fjord in the Canadian Arctic to reconstruct the retreat chronology of an outlet glacier of the Laurentide ice sheet, following the last glacial termination. We find that Sam Ford Fjord, which has a similar morphology to the troughs holding many outlet glaciers of the Greenland ice sheet, was rapidly deglaciated about 9,500 years ago, with retreat rates ranging from 5 to 58 m yr^-1. The highest rates occurred in the deepest part of the fjord (900 m), whereas regions beyond the fjord mouth and up-valley of the head of the fjord experienced the lowest rates of retreat. We conclude that in such a fjord setting, there is a strong bathymetric control on the retreat of marine outlet glaciers: once the terminus of the outlet glacier retreated into deeper waters, increasing calving rates and basal sliding speeds caused the glacier to rapidly thin and retreat, stabilizing only when it reached the shallow inland head of the fjord.