We study the evolution of tropospheric ozone over the period 1979–2010 using a chemistry‐climate model employing a stratosphere‐troposphere chemistry scheme. By running with specified dynamics, the key feedback of composition on meteorology is suppressed, isolating the chemical response. By using historical forcings and emissions, interactions between processes are realistically represented. We use the model to assess how the ozone responds over time and to investigate model responses and trends. We find that the chlorofluorocarbon (CFC)‐driven decrease in stratospheric ozone plays a significant role in the tropospheric ozone burden. Over the period 1979–1994, the decline in transport of ozone from the stratosphere, partially offsets an emissions‐driven increase in tropospheric ozone production. From 1994–2010, despite a leveling off in emissions, increased stratosphere‐to‐troposphere transport of ozone drives a small increase in the tropospheric ozone burden. These results have implications for the impact of future stratospheric ozone recovery on air quality and radiative forcing. Plain Language Summary We use a modeling approach to study the effect of stratospheric ozone depletion on the composition of the troposphere. We focus on the period 1979–2010 and use a chemistry‐climate model employing historical emissions, climate forcing, and meteorology. Our model has a good description of both stratospheric and tropospheric ozone chemistry and allows us to calculate the effect of exchange between stratosphere and troposphere. We show that stratospheric ozone depletion over the period 1979–2010 has a critical effect on tropospheric composition – with less ozone in the lower stratosphere, there is less transport to the troposphere, and this offsets an emissions‐driven increase in ozone production in the troposphere. Such combined studies are important to quantify the future effects of stratospheric ozone recovery on the evolution of tropospheric composition. Key Points We show that stratospheric ozone recovery has an affect on tropospheric ozone levels Stratospheric ozone loss over the period 1979–1994 offset an emissions‐driven increase in tropospheric ozone Future stratospheric ozone recovery and changes to the rate of stratosphere‐to‐troposphere transport will be important in the future