Atmospheric circulation teleconnections play a critical role in modulating low-frequency climate variability and driving regional extreme weather events, such as summer heatwaves. However, traditional teleconnection indices are predominantly defined using two-dimensional horizontal variables, which inadequately represent the dynamically crucial coupled vertical circulations. Here, we establish a three-dimensional analytical framework by applying the teleconnection method to the meridional and zonal vertical stream functions (H and W) derived from the three-pattern decomposition of global atmospheric circulation (3P-DGAC). We identify 14 structurally distinct vertical teleconnection patterns in the Northern Hemisphere mid-high latitudes, which demonstrate robust validity in reconstructing summer surface air temperature (SAT) and hemispheric circulation fields (yielding mean spatial correlations of 0.64 and 0.60, respectively, over 1979–2022). The proposed three-dimensional teleconnections effectively capture the low-frequency atmospheric variability that modulates Northern Hemisphere summer climate. Ultimately, this framework provides a unified dynamical perspective for understanding seasonal climate variability and offers a robust approach for diagnosing the atmospheric circulation mechanisms underlying regional temperature extremes.