The Greenland Ice Sheet holds 7.2 m of sea level equivalent and in recent decades, rising temperatures have led to accelerated mass loss. Current ice margin recession is led by the retreat of outlet glaciers, large rivers of ice ending in narrow fjords that drain the interior. We pair an outlet glacier–resolving ice sheet model with a comprehensive uncertainty quantification to estimate Greenland’s contribution to sea level over the next millennium. We find that Greenland could contribute 5 to 33 cm to sea level by 2100, with discharge from outlet glaciers contributing 8 to 45% of total mass loss. Our analysis shows that uncertainties in projecting mass loss are dominated by uncertainties in climate scenarios and surface processes, whereas uncertainties in calving and frontal melt play a minor role. We project that Greenland will very likely become ice free within a millennium without substantial reductions in greenhouse gas emissions.