The Labrador Sea is one of the sites where convection exports surface water to the deep ocean in winter as part of the thermohaline circulation. Labrador Sea water is characteristically cold and fresh, and it can be traced at intermediate depths (500-2,000 m) across the North Atlantic Ocean, to the south and to the east of the Labrador Sea. Widespread observations of the ocean currents that lead to this distribution of Labrador Sea water have, however, been difficult and therefore scarce. We have used more than 200 subsurface floats to measure directly basin-wide horizontal velocities at various depths in the Labrador and Irminger seas. We observe unanticipated recirculations of the mid-depth (approximately 700 m) cyclonic boundary currents in both basins, leading to an anticyclonic flow in the interior of the Labrador basin. About 40% of the floats from the region of deep convection left the basin within one year and were rapidly transported in the anticyclonic flow to the Irminger basin, and also eastwards into the subpolar gyre. Surprisingly, the float tracks did not clearly depict the deep western boundary current, which is the expected main pathway of Labrador Sea water in the thermohaline circulation. Rather, the flow along the boundary near Flemish Cap is dominated by eddies that transport water offshore. Our detailed observations of the velocity structure with a high data coverage suggest that we may have to revise our picture of the formation and spreading of Labrador Sea water, and future studies with similar instrumentation will allow new insights on the intermediate depth ocean circulation.