An influence of solar irradiance variations on Earth’s surface climate has been repeatedly suggested, based on correlations between solar variability and meteorological variables. Specifically, weaker westerly winds have been observed in winters with a less active sun, for example at the minimum phase of the 11-year sunspot cycle. With some possible exceptions, it has proved difficult for climate models to consistently reproduce this signal. Spectral Irradiance Monitor satellite measurements indicate that variations in solar ultraviolet irradiance may be larger than previously thought. Here we drive an ocean–atmosphere climate model with ultraviolet irradiance variations based on these observations. We find that the model responds to the solar minimum with patterns in surface pressure and temperature that resemble the negative phase of the North Atlantic or Arctic Oscillation, of similar magnitude to observations. In our model, the anomalies descend through the depth of the extratropical winter atmosphere. If the updated measurements of solar ultraviolet irradiance are correct, low solar activity, as observed during recent years, drives cold winters in northern Europe and the United States, and mild winters over southern Europe and Canada, with little direct change in globally averaged temperature. Given the quasiregularity of the 11-year solar cycle, our findings may help improve decadal climate predictions for highly populated extratropical regions.