The most marked step in the global climate transition from "Greenhouse" to "Icehouse" Earth occurred at the Eocene-Oligocene (E-O) boundary, 33.7 Ma. Evidence for climatic changes comes from many sources, including the marine benthic delta18O record, showing an increase by 1.2-1.50/00 at this time. This positive excursion is characterised by two steps, separated by a plateau. The increase in delta18O values has been attributed to rapid glaciation of the Antarctic continent, previously ice-free. Simultaneous changes in the delta13C record are suggestive of a greenhouse gas control on climate. Previous modelling studies show that a decline in pCO2 beyond a certain threshold value may have initiated the growth of a Southern Hemispheric ice sheet. These studies were not able to conclusively explain the remarkable two-step profile in delta18O. Furthermore, they considered changes in the ocean circulation only regionally, or indirectly through the oceanic heat transport. The potential role of global changes in ocean circulation in the E-O transition has not been addressed yet. Here a new interpretation of the delta18O signal is presented, based on model simulations using a simple coupled 8-box-ocean, 4-box-atmosphere model with an added land ice component. The model was forced with a slowly decreasing atmospheric carbon dioxide concentration. It is argued that the first step in the delta18O record reflects a shift in meridional overturning circulation from a Southern Ocean to a bipolar source of deep-water formation, which is associated with a cooling of the deep sea. The second step in the delta18O profile occurs due to a rapid glaciation of the Antarctic continent. This new mechanism is a robust outcome of our model and is qualitatively in close agreement with proxy data.