From the Eocene (~50 million years ago) to today, Southern Ocean circulation has evolved from the existence of two ocean gyres to the dominance of the Antarctic Circumpolar Current (ACC). It has generally been thought that the opening of Southern Ocean gateways in the late Eocene, in addition to the alignment of westerly winds with these gateways or the presence of Antarctic ice sheet, was a sufficient requirement for the transition to an ACC of similar strength to its modern equivalent. Nevertheless, models representing these changes produce only a much weaker ACC. Here we show, using an eddying ocean model, that the missing ingredient in the transition to a modern ACC is deep convection around the Antarctic continent. This deep convection is caused by cold temperatures and high salinities due to sea-ice production around the Antarctic continent, leading to both the formation of Antarctic Bottom Water and a modern-strength ACC.