A significant correlation between the annual cosmic ray flux and the amount of low clouds has recently been found for the past 20 years. However, of the physical explanations suggested, none has been quantitatively verified in the atmosphere by a combination of modelling and experiment. Here we study the relation between the global distributions of the observed low cloud amount and the calculated tropospheric ionization induced by cosmic rays. We find that the time evolution of the low cloud amount can be decomposed into a long-term trend and inter-annual variations, the latter depicting a clear 11-year cycle. We also find that the relative inter-annual variability in low cloud amount increases polewards and exhibits a highly significant one-to-one relation with inter-annual variations in the ionization over the latitude range 20 - 55degreesS and 10 - 70 degreesN. This latitudinal dependence gives strong support for the hypothesis that the cosmic ray induced ionization modulates cloud properties.