On the East Greenland Shelf, downwelling-favorable northerly winds confine the freshest water masses to the inner shelf, creating a strong cross-shelf salinity gradient. This wedge of fresh water supports a southward East Greenland Coastal Current (EGCC) that flows continuously from Fram Strait (80°N) to Cape Farewell at the southern tip of Greenland (60°N). What happens to this freshwater as it rounds Cape Farewell is not well understood. Here, we present results from a Lagrangian experiment in which we deployed 50 Surface Velocity Program (SVP) drifters and 8 profiling floats in the EGCC on the southeast Greenland shelf in August/September 2021 and 2022. The SVP drifters were drogued at 15 m and the profiling floats drifted at 100 m for 6 hours and profiled to the surface every 6 hours. We find that the vast majority of the EGCC continues on the shelf around Cape Farewell and supplies the northward West Greenland Coastal Current (WGCC). Local winds exert strong control on the coastal current’s cross-shelf position, but there is little evidence of shelf-basin exchange there. Investigation of the winds during the deployments revealed that they were similar to the mean conditions, and thus our instruments likely captured the typical ocean circulation. However, the lack of sampling during a strong Greenland tip jet event leaves open the possibility that the shelf-basin exchange in this region is intermittent in response to large wind events.