Arctic‐origin and Greenland meltwaters circulate cyclonically in the boundary current system encircling the Labrador Sea. The ability of this freshwater to penetrate the interior basin has important consequences for dense water formation and the lower limb of the Atlantic Meridional Overturning Circulation. However, the precise mechanisms by which the freshwater is transported offshore, and the magnitude of this flux, remain uncertain. Here, we investigate wind‐driven upwelling northwest of Cape Farewell using 4 years of high‐resolution data from the Overturning in the Subpolar North Atlantic Program west Greenland mooring array, deployed from September 2014–2018, along with Argo, shipboard, and atmospheric reanalysis data. A total of 49 upwelling events were identified corresponding to enhanced northwesterly winds, followed by reduced along‐stream flow of the boundary current and anomalously dense water present on the outer shelf. The events occur during the development stage of forward Greenland tip jets. During the storms, a cross‐stream Ekman cell develops that transports freshwater offshore in the surface layer and warm, saline, Atlantic‐origin waters onshore at depth. The net fluxes of heat and freshwater for a representative storm are computed. Using a one‐dimensional mixing model, it is shown that the freshwater input resulting from the locus of winter storms could significantly limit the wintertime development of the mixed layer and hence the production of Labrador Sea Water in the southeastern part of the basin.