Based on ERA-Interim and JRA-55 daily reanalysis datasets, connections among the variations in the Brewer–Dobson circulation (BDC) intensity, stratospheric air mass, surface pressure, and the tropospheric meridional circulation during the period from 1979 to 2015 are analyzed. The results show that the variations in the surface pressure, particularly at middle and high latitudes, have a close correlation with the variations in the stratospheric BDC intensity. When the upwelling at 450 K intensifies, the surface pressure increases in the high latitudes (poleward of 60°) and decreases in the adjacent mid-latitudes in both hemispheres. And these correlations are most significant during boreal winter in the Northern Hemisphere and during austral autumn in the Southern Hemisphere. It is found that the high latitude surface pressure changes follow the anomalous BDC by about 30 days. The increase in polar surface pressure associated with the stronger BDC is due to an increase in stratospheric air mass, while the decrease in mid-latitude surface pressure is related to a decrease in tropospheric air mass. These air mass changes are caused by the anomalous meridional transport of air mass by the residual mean circulation in the stratosphere and troposphere. In addition, we found a significant connection between the intensity of the BDC and the Ferrel cell, i.e., when the BDC strengthens (weakens), there is a weakened (strengthened) Ferrel cell with its position shifting equatorward (poleward).