Southern Hemisphere (SH) Stratospheric Warming Events (SWEs) are usually associated with a negative phase of the tropospheric Southern Annular Mode (SAM) during the following summer. In contrast, using ensemble climate model simulations we show that the anomalously high ozone concentrations typically occurring during SWEs can force periods of persistent positive tropospheric SAM in austral spring by increasing lower stratospheric static stability and changing troposphere-to-stratosphere wave propagation. Eventually, the tropospheric SAM switches sign to its negative phase in late spring/early summer, but this ‘downward propagation’ of the stratospheric signal does not occur in simulations without seasonal cycle. We find that the downward propagation is forced both dynamically by adiabatic heating and radiatively by increased shortwave absorption by ozone due to the seasonal cycle. Capturing this ozone forcing mechanism in models requires the inclusion of interactive ozone, which has important implications for the predictive skill of current seasonal forecasting systems.