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While reasonable knowledge of multidecadal Arctic freshwater storage variability exists, we have little knowledge of Arctic freshwater exports on similar time scales. A hydrographic time series from the Labrador Shelf, spanning seven decades at annual resolution, is here used to quantify Arctic Ocean freshwater export variability west of Greenland. Output from a high-resolution coupled ice–ocean model is used to establish the representativeness of those hydrographic sections. Clear annual to decadal variability emerges, with high freshwater transports during the 1950s and 1970s–80s, and low transports in the 1960s and from the mid-1990s to 2016, with typical amplitudes of 30 mSv (1 Sv = 106m3s−1). The variability in both the transports and cumulative volumes correlates well both with Arctic and North Atlantic freshwater storage changes on the same time scale. We refer to the “inshore branch” of the Labrador Current as the Labrador Coastal Current, because it is a dynamically and geographically distinct feature. It originates as the Hudson Bay outflow, and preserves variability from river runoff into the Hudson Bay catchment. We find a need for parallel, long-term freshwater transport measurements from Fram and Davis Straits to better understand Arctic freshwater export control mechanisms and partitioning of variability between routes west and east of Greenland, and a need for better knowledge and understanding of year-round (solid and liquid) freshwater fluxes on the Labrador shelf. Our results have implications for wider, coherent atmospheric control on freshwater fluxes and content across the Arctic Ocean and northern North Atlantic Ocean.