There are three fundamental features which characterize large glacial millennial (Dansgaard‐Oeschger) oscillations: (1) the climatic transitions were abrupt and large; (2) the lengths of both interstadials and stadials and the period of Dansgaard‐Oeschger oscillations were not uniform; and (3) there were no large millennial oscillations during an early stage of a glacial period and a peak glacial period. In this modeling study we offer a consistent explanation for these three features by employing an Earth system Model of Intermediate Complexity. We demonstrate that a moderate global cooling forces the Atlantic meridional overturning circulation (MOC) into an unstable state and hence causes the flip‐flop of the Atlantic MOC between a strong mode and a weak mode. The durations of both interstadials and stadials associated with these millennial oscillations are modulated by the changing background climate in qualitative agreement with the observations. In a warm climate the Atlantic MOC is strong and stable, with the deep water formed mainly by intense heat loss to the atmosphere. In a cold climate the Atlantic MOC is weak and stable, and this mode is largely maintained by the process of sea ice brine rejection. Since the Dansgaard‐Oeschger oscillations result from an alternation between these two MOC states during an intermediate phase climate, we conclude that brine rejection plays a necessary role in the oscillations, confirming a hypothesis suggested in some proxy data studies.