Now that stratospheric ozone depletion has been controlled by the Montreal Protocol1, interest has turned to the effects of climate change on the ozone layer2,3. Climate models predict an accelerated stratospheric circulation4,5,6, leading to changes in the spatial distribution of stratospheric ozone2,7 and an increased stratosphere-to-troposphere ozone flux8,9. Here we use an atmospheric chemistry climate model to isolate the effects of climate change from those of ozone depletion and recovery on stratosphere-to-troposphere ozone flux and the clear-sky ultraviolet radiation index—a measure of potential human exposure to ultraviolet radiation. We show that under the Intergovernmental Panel on Climate Change moderate emissions scenario10, global stratosphere-to-troposphere ozone flux increases by 23% between 1965 and 2095 as a result of climate change. During this time, the clear-sky ultraviolet radiation index decreases by 9% in northern high latitudes—a much larger effect than that of stratospheric ozone recovery—and increases by 4% in the tropics, and by up to 20% in southern high latitudes in late spring and early summer. The latter increase in the ultraviolet index is equivalent to nearly half of that generated by the Antarctic ‘ozone hole’ that was created by anthropogenic halogens. Our results suggest that climate change will alter the tropospheric ozone budget and the ultraviolet index, which would have consequences for tropospheric radiative forcing11, air quality8 and human and ecosystem health12.