Stratospheric aerosol clouds from large tropical volcanic eruptions can be expected to alter the atmospheric radiative balance for a period of up to several years. Observations following several previous major eruptions suggest that one effect of the radiative perturbations is to cause anomalies in the Northern Hemisphere extratropical winter tropospheric circulation that can be broadly characterized as positive excursions of the Arctic Oscillation (AO). We report on a modeling investigation of the radiative and dynamical mechanisms that may account for the observed AO anomalies following eruptions. We focus on the best observed and strongest 20th century eruption, that of Mt. Pinatubo on 15 June 1991. The impact of the Pinatubo eruption on the climate has been the focus of a number of earlier modeling studies, but all of these previous studies used models with no quasi‐biennial oscillation (QBO) in the tropical stratosphere. The QBO is a very prominent feature of interannual variability of tropical stratospheric circulation and could have a profound effect on the global atmospheric response to volcanic radiative forcing. Thus a complete study of the atmospheric variability following volcanic eruptions should include a realistic representation of the tropical QBO. Here we address, for the first time, this important issue. We employed a version of the SKYHI troposphere‐stratosphere‐mesosphere model that effectively assimilates observed zonal mean winds in the tropical stratosphere to simulate a very realistic QBO. We performed an ensemble of 24 simulations for the period 1 June 1991 to 31 May 1993. These simulations included a realistic prescription of the stratospheric aerosol layer based on satellite observations. These integrations are compared to control integrations with no volcanic aerosol. The model produced a reasonably realistic representation of the positive AO response in boreal winter that is usually observed after major eruptions. Detailed analysis shows that the aerosol perturbations to the tropospheric winter circulation are affected significantly by the phase of the QBO, with a westerly QBO phase in the lower stratosphere resulting in an enhancement of the aerosol effect on the AO. Improved quantification of the QBO effect on climate sensitivity helps to better understand mechanisms of the stratospheric contribution to natural and externally forced climate variability.