Amidst stormy atmospheric circulation, there are prominent recurrent patterns of variability in the southern and northern hemispheres, now often known as Antarctic Oscillation (AAO) and Arctic Oscillation (AO) or North Atlantic Oscillation (NAO). Their climatological, ecological and societal impacts have being subjects of active research. However, a unique theory for the origin of these dominant climate patterns is so far absent, and is herein proposed. The atmospheric internal dynamics allow anomalous global-scale circulations of AO and AAO structures to organize the abundant synoptic eddies in the turbulent atmospheric circulation such that the former can be selectively reinforced. This dynamic self-organization of the AO and AAO makes them the leading modes of variability in the extratropical climate.