Ozone depletion led to a positive trend in the summertime Southern Annular Mode (SAM) during the last decades of the 20th century. During the present century, global warming (GW) is expected to contribute to a positive SAM trend while ozone recovery is expected to act in the opposite direction. Here, Southern Hemisphere (SH) circulation and regional precipitation change are studied with a methodology that separates the effects from GW and ozone depletion/recovery. Our results show that a “tug‐of‐war” between ozone and GW occurs in the summertime stratosphere, propagating to the troposphere where it is manifest in the SAM. However, at the regional scale this “tug‐of‐war” is not as relevant as the combined effects of other remote drivers of circulation change, which force different kinds of precipitation changes in the SH. For regional precipitation changes, the uncertainty in future circulation change is as important as the uncertainty in the GW level. Plain Language Summary In the Southern Hemisphere, both ozone depletion and global warming have influenced climate in the past decades. Ozone recovery is expected to reverse the influence of ozone depletion, but the influence of global warming is expected to grow. Here, we investigate the combined effects of these anthropogenic forcings through the second half of the 20th century and the entire 21st century, quantifying their influence on stratospheric and tropospheric circulation and on regional precipitation changes. We find that the summertime stratosphere is affected by a “tug‐of‐war” between these two forcings, and that its effect propagates downward to the tropospheric circulation. On the other hand, summer precipitation in the land areas of the SH that are expected to experience large effects of climate change are not strongly affected by this “tug‐of‐war,” but are instead influenced by the effects of both stratospheric and tropical tropospheric changes. Key Points Long‐term changes in the delay of the breakdown of the Southern Hemisphere stratospheric polar vortex can be largely explained by a linear response to ozone‐depleting substances and to global warming The tug‐of‐war between ozone recovery and global warming manifests itself in the stratospheric vortex breakdown delay and propagates to the troposphere The uncertainty in future changes in regional precipitation in the Southern Hemisphere is subject to the combined effects of the uncertainty in tropical warming and in the vortex breakdown delay