During the Eocene-Oligocene transition, the meridional overturning circulation underwent large changes, associated with the geological evolution of Southern Ocean gateways. These are crucial for the Cenozoic climate transition from Greenhouse to Icehouse, but their dynamics still remain elusive. We demonstrate, using an idealised eddying ocean model, that the opening of a gateway leads to an abrupt onset of a vigorous, deep-reaching, meridional overturning circulation. This meridional overturning circulation has a maximum transport for a shallow gateway, and decreases with further deepening of the gateway. This abrupt change in the meridional overturning circulation can be explained through the ability with which standing meanders -- turbulent features located downstream of the gateway -- can induce deep vertical heat transport at high latitudes where bottom waters are produced. Our results demonstrate the crucial role of turbulent processes, associated with tectonic evolution, in setting the strength of the global ocean's deep-reaching meridional overturning circulation.