Declining atmospheric CO₂ concentrations are considered the primary driver for the Cenozoic Greenhouse-Icehouse transition, ~34 million years ago. A role for tectonically opening Southern Ocean gateways, initiating the onset of a thermally isolating Antarctic Circumpolar Current, has been disputed as ocean models have not reproduced expected heat transport to the Antarctic coast. Here we use high-resolution ocean simulations with detailed paleobathymetry to demonstrate that tectonics did play a fundamental role in reorganising Southern Ocean circulation patterns and heat transport, consistent with available proxy data. When at least one gateway (Tasmanian or Drake) is shallow (300 m), gyres transport warm waters towards Antarctica. When the second gateway subsides below 300 m, these gyres weaken and cause a dramatic cooling (average of 2-4 Celsius degree, up to 5 Celsius degree) of Antarctic surface waters whilst the ACC remains weak. Our results demonstrate that tectonic changes are crucial for Southern Ocean climate change and should be carefully considered in constraining long-term climate sensitivity to CO₂.