The atmospheric response to the Kuroshio Extension (KE) variability during 1979-2012 is investigated using a KE index derived from sea surface height measurements and an eddy-resolving ocean general circulation model hindcast. When the index is positive, the KE is in the stable state, strengthened and shifted northward, with lower eddy kinetic energy, and the Kuroshio-Oyashio Extension (KOE) region is anomalously warm. The reverse holds when the index is negative. Regression analysis shows that there is a coherent atmospheric response to the decadal KE fluctuations between October and January. The KOE warming generates an upward surface heat flux that leads to local ascending motions and a northeastward shift of the zones of maximum baroclinicity, eddy heat and moisture fluxes, and the storm track. The atmospheric response consists of an equivalent barotropic large-scale signal, with a downstream high and a low over the Arctic. The heating and transient eddy anomalies excite stationary Rossby waves that propagate the signal poleward and eastward. There is a warming typically exceeding 0.6 K at 900 hPa over eastern Asia and western United States, which reduces the snow cover by 4%-6%. One month later, in November-February, a high appears over northwestern Europe, and the hemispheric teleconnection bears some similarity with the Arctic Oscillation. Composite analysis shows that the atmospheric response primarily occurs during the stable state of the KE, while no evidence of a significant large-scale atmospheric response is found in the unstable state. Arguments are given to explain this strong asymmetry.