The Greenland ice sheet (GrIS) stores the largest amount of freshwater in the Northern Hemisphere and has been recently losing mass at an increasing rate. An eddy‐permitting ocean general circulation model is forced with realistic estimates of freshwater flux from the GrIS. Two approaches are used to track the meltwater and its trajectory in the ocean. We show that freshwater from western and eastern GrIS have markedly different fates, on a decadal time scale. Freshwater from west Greenland predominantly accumulates in Baffin Bay before being exported south down the Labrador shelf. Meanwhile, GrIS freshwater entering the interior of the Labrador Sea, where deep convection occurs, comes predominantly (∼80%) from east Greenland. Therefore, hosing experiments, which generally assume a uniform freshwater flux spatially, will not capture the true hydrographic response and regional impacts. In addition, narrow boundary currents are important for freshwater transport and distribution, requiring simulations with eddy‐resolving resolution.