MANY recent studies have reported an apparent correlation between solar activity and the Earth’s climate on the timescale of the ii-year solar cycle(1-4) and over longer periods(5-10), but to date no physical mechanism has been proposed that can satisfactorily explain the observations. In general, it has been assumed that changes in total solar irradiance outside the atmosphere will be reflected in proportionately equal changes at the tropopause (from where the influence on climate is determined). Here I present results from a two-dimensional radiative-chemical-transport model which show that the spectral composition of the solar variations and the photochemical production of stratospheric ozone together lead to a highly nonlinear relationship between the extraterrestrial and cross-tropopause solar radiative flux. Because of this relationship, at middle to high latitudes in the winter hemisphere less solar radiation reaches the troposphere during periods of higher solar activity. The consequent change in latitudinal temperature gradient also affects infrared radiative forcing and potentially planetary-wave activity. The general mechanism proposed here may explain some features of the observed correlations between solar variability and climate.