Future changes in the stratospheric circulation could have an important impact on northern winter tropospheric climate change, given that sea level pressure (SLP) responds not only to tropospheric circulation variations but also to vertically coherent variations in troposphere‐stratosphere circulation. Here we assess northern winter stratospheric change and its potential to influence surface climate change in the Coupled Model Intercomparison Project‐Phase 5 (CMIP5) multimodel ensemble. In the stratosphere at high latitudes, an easterly change in zonally averaged zonal wind is found for the majority of the CMIP5 models, under the Representative Concentration Pathway 8.5 scenario. Comparable results are also found in the 1% CO2 increase per year projections, indicating that the stratospheric easterly change is common feature in future climate projections. This stratospheric wind change, however, shows a significant spread among the models. By using linear regression, we quantify the impact of tropical upper troposphere warming, polar amplification, and the stratospheric wind change on SLP. We find that the intermodel spread in stratospheric wind change contributes substantially to the intermodel spread in Arctic SLP change. The role of the stratosphere in determining part of the spread in SLP change is supported by the fact that the SLP change lags the stratospheric zonally averaged wind change. Taken together, these findings provide further support for the importance of simulating the coupling between the stratosphere and the troposphere, to narrow the uncertainty in the future projection of tropospheric circulation changes.