Changes in stratospheric ozone concentrations and increasing concentrations of greenhouse gases (GHGs) alter the temperature structure of the atmosphere and drive changes in the atmospheric and oceanic circulation. We systematically investigate the impacts of ozone recovery and increasing GHGs on the atmospheric and oceanic circulation in the Southern Hemisphere during the twenty-first century using a unique coupled ocean–atmosphere climate model with interactive ozone chemistry and enhanced oceanic resolution. We use the high-emission scenario SSP5-8.5 for GHGs under which the springtime Antarctic total column ozone returns to 1980s levels by 2048 in our model, warming the lower stratosphere and strengthening the stratospheric westerly winds. We perform a spatial analysis and show for the first time that the austral spring stratospheric response to GHGs exhibits a marked planetary wavenumber 1 (PW1) pattern, which reinforces the response to ozone recovery over the Western Hemisphere and weakens it over the Eastern Hemisphere. These changes, which imply an eastward phase shift in the PW1, largely cancel out in the zonal mean. The Southern Hemisphere residual circulation strengthens during most of the year due to the increase in GHGs and weakens in spring due to ozone recovery. However, we find that in November the GHGs also drive a weakening of the residual circulation, reinforcing the effect of ozone recovery, which represents another novel result. At the surface, the westerly winds weaken and shift equatorward due to ozone recovery, driving a weak decrease in the transport of the Antarctic Circumpolar Current and in the Agulhas leakage and a cooling of the upper ocean, which is most pronounced in the latitudinal band 35–45∘ S. The increasing GHGs drive changes in the opposite direction that overwhelm the ozone effect. The total changes at the surface and in the oceanic circulation are nevertheless weaker in the presence of ozone recovery than those induced by GHGs alone, highlighting the importance of the Montreal Protocol in mitigating some of the impacts of climate change. We additionally compare the combined effect of interactively calculated ozone recovery and increasing GHGs with their combined effect in an ensemble in which we prescribe the CMIP6 ozone field. This second ensemble simulates a weaker ozone effect in all the examined fields, consistent with its weaker increase in ozone. The magnitude of the difference between the simulated changes at the surface and in the oceanic circulation in the two ensembles is as large as the ozone effect itself. This shows the large uncertainty that is associated with the choice of the ozone field and how the ozone is treated.