The intricate near‐circumpolar system of fronts and currents surrounding Antarctica isolates much of Earth's freshwater from the saline oceans immediately north. The Antarctic Slope Front sustains bathymetrically steered flow at the shelf break, whereas the shallow Coastal Current travels rapidly alongside the ice front. A hydrographic survey of the southeastern Weddell Sea finds these two features to have merged near the narrow (<40 km wide) continental shelf at Fimbulisen. On the prime meridian, its Trolltunga ice tongue overshoots the shelf break northward into this slope current. Observations on either side of the ice tongue demonstrate its retarding effect on the westward‐flowing waters it overhangs and its contribution to the poorly understood freshwater budget. From oxygen isotope ratio measurements and referenced geostrophic shears, we find the combined glacial meltwater and sea ice melt transport upstream of Trolltunga at 0.6°E to account for 18.0 ± 5.8 mSv of the total 1.6 ± 0.2 Sv westward transport (Sv = 106 m3 s−1). In Trolltunga's lee and downstream at 2.8°W, we find this figure to ultimately increase to 23.8 ± 15.5 mSv of a total 2.8 ± 0.4 Sv transport. Each of these sections was impeded by sea ice cover, so these estimates of westward transport are probably lower limits. The westward glacial ice meltwater transport of 10 ± 3 mSv at 2.8°W highlights the role that Fimbulisen plays in preconditioning shelf waters before they reach broad continental shelves in the southwestern Weddell Sea where they transform to bottom waters.