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Numerous studies have suggested an impact of the 11 year solar cycle on the winter North Atlantic Oscillation (NAO), with an increased tendency for positive (negative) NAO signals to occur at maxima (minima) of the solar cycle. Climate models have successfully reproduced this solar cycle modulation of the NAO, although the magnitude of the effect is often considerably weaker than implied by observations. A leading candidate for the mechanism of solar influence is via the impact of ultraviolet radiation variability on heating rates in the tropical upper stratosphere, and consequently on the meridional temperature gradient and zonal winds. Model simulations show a zonal mean wind anomaly that migrates polewards and downwards through wave–mean flow interaction. On reaching the troposphere this produces a response similar to the winter NAO. Recent analyses of observations have shown that solar cycle–NAO link becomes clearer approximately three years after solar maximum and minimum. Previous modelling studies have been unable to reproduce a lagged response of the observed magnitude. In this study, the impact of solar cycle on the NAO is investigated using an atmosphere–ocean coupled climate model. Simulations that include climate forcings are performed over the period 1960–2009 for two solar forcing scenarios: constant solar irradiance, and time-varying solar irradiance. We show that the model produces significant NAO responses peaking several years after extrema of the solar cycle, persisting even when the solar forcing becomes neutral. This confirms suggestions of a further component to the solar influence on the NAO beyond direct atmospheric heating and its dynamical response. Analysis of simulated upper ocean temperature anomalies confirms that the North Atlantic Ocean provides the memory of the solar forcing required to produce the lagged NAO response. These results have implications for improving skill in decadal predictions of the European and North American winter climate.