Rapidly accumulating sediments from the Björn drift deposit south of Iceland are studied for comparison of glacial/interglacial climate changes related to millennial variability of the subpolar surface and deep ocean circulation in the North Atlantic. High‐resolution faunal, isotopic, and sedimentary analyses reveal a strong multimillennial climatic variability interpreted as oscillations in heat transport westward south of Iceland during marine isotope stage 6 (MIS 6), possibly related to the strength of the subpolar gyre (SPG). The oscillations persisted from MIS 6 through the following interglacial (MIS 5), although with diminished magnitude, and were respectively characterized by repeated advances of the polar front south of Iceland during MIS 6 and southward migrations of the Arctic front due to cold surface outflow through the East Greenland and East Iceland Currents during MIS 5. Incursions of cold, fresh surface waters, and drifting ice affected the dynamics of the SPG, episodically causing it to weaken and contract to the northwest. During these intervals of diminished SPG, the northward transport of subtropical heat and salt was strengthened and preferentially conveyed to the northeast past Iceland, enhancing deep‐water formation in the Nordic Seas. By contrast, when the SPG was strong, more subtropical water and its associated heat were entrained within the relatively warm Irminger Current flowing westward south of Iceland. These oceanographic oscillations were associated with repeated multimillennial cooling and warming episodes during the glacial stage MIS 6, equivalent to the Dansgaard‐Oeschger cycles of the last glaciation.