Sites of ice-stream discharge to the continental slope build trough-mouth fans from glacigenic debris flows (GDFs), subglacial meltwater flows, and suspended sediment. Thus, past ice configurations may be interpreted from the sedimentological record. This study links the records in cores, high-resolution seismic profiles, and multibeam swath bathymetry of Hatton Slope and Fan to the changing glaciological history in Hudson Strait, one of the largest ice streams of the late Pleistocene Laurentide Ice Sheet. 14C-AMS dates, X-ray fluorescence geochemical profiles, and oxygen isotopes in sixteen cores document sediment supply during the last glacial cycle, and earlier history is interpreted from seismic data. The Frobisher Bay slope sector has a long record of GDF deposits from severe glacial periods between MIS 6 and 22, with little impact of meltwater discharge. Mass-transport events and aggrading gravel-floored valleys dominate the northern Hatton slope sector. The central slope sector shows the greatest shelf break progradation by till deposition, with kilometre-spaced gullies heading at 700–730 mbsl from the last major grounding of the ice-stream on the upper slope during Heinrich event 3 (H3). The gullies pass downslope into ∼5 km wide valleys, which have been sites of sediment bypass since widespread meltwater flow in MIS 6 and show little aggradation since MIS 16. Intervening >50 m high ridges show alternating levee accretion and erosion by shallow mass-transport events. Downslope on Hatton Fan, GDFs are common and fill wide erosional channels that lead to the sandy braid plain of the central Labrador Sea. The channels of the southern sector and Saglek Slope have channeled turbidity currents down the NAMOC, and stratified contourite deposits accumulated on the fan. Over the MIS 1–3 period widely represented by cores, ice was grounded in Hatton Basin and on the upper slope to 700 m water depth only immediately prior to H3. Older and younger H events had a floating ice-shelf in Hatton Basin, and sedimentation was dominated by the retreat of that ice shelf to Resolution Island. Distal cores show no systematic difference between the H1–top H3 interval and the base H3–H5 interval. Given the supply of carbonate detritus of consistent composition back to at least H5, any MIS 3 deglaciation of Hudson Bay would require improbably high growth rates of ice sheets in the centre of the continent.