Atmospheric processes of tropospheric origin can perturb the stratosphere, but direct feedback in the opposite direction is usually assumed to be negligible, despite the troposphere＇s sensitivity to changes in the release of wave activity into the stratosphere(1-3). Here, however, we present evidence that such a feedback exists and can be significant. We find that if the wintertime Arctic polar stratospheric vortex is distorted, either by waves propagating upward from the troposphere(4) or by eastward-travelling stratospheric waves(5,6), then there is a concomitant redistribution of stratospheric potential vorticity which induces perturbations in key meteorological fields in the upper troposphere. The feedback is large despite the much greater mass of the troposphere : it can account for up to half of the geopotential height anomaly at the tropopause. Although the relative strength of the feedback is partly due to a cancellation(7) between contributions to these anomalies from lower altitudes, our results imply that stratospheric dynamics and its feedback on the troposphere are more significant for climate modelling and data assimilation than was previously assumed.