Numerical simulations of the Atlantic and Arctic Oceans using an ocean-sea ice model are analysed with respect to interannual-to-decadal variability (1948–2008) of the dense water overflows east and west of Iceland. Besides the good agreement between observed and simulated Denmark Strait and Faroe-Bank Channel overflows, the model shows an antiphase relation between both transports at time scales of 3–10 yr. The analysis of wind stress curl over the Nordic Seas suggests that the phase relation is locally forced. The main mode of atmospheric variability in the Atlantic reinforces the dense overflow west of Iceland during positive phases of the North Atlantic Oscillation (NAO) and decreases it during negative phases. East of Iceland the overflow is decreased during positive phases of the NAO and increased during negative phases. After the mid-1990s, the antiphase relation is less clear due to a reduction of wind stress curl variance and a change in the production of dense water in the Nordic Seas. In that period, the Norwegian Sea experienced a reduction of its cyclonicity, leading to the export of a surplus of dense water across the Faroe-Shetland Channel. The forcing of the gyre variability is attributed to large-scale wind stress curl changes and to shifts of convection regimes linked to Arctic-Nordic Seas dense water exchange modifications at Fram Strait. Simulated sea surface height variability is highly correlated with the dense water volume in the Greenland and Norwegian Seas gyres, implying that altimetric measurements are good indicators of dense water content in the Nordic Seas and therefore provide a potential for monitoring the reservoirs and explain/anticipate changes in the overflows.