The opening of the Drake Passage (DP) during the Cenozoic is a tectonic event of paramount importance for the development of modern ocean characteristics. Notably, it has been suggested that it exerts a primary role in the onset of the Antarctic Circumpolar Current (ACC) formation, in the cooling of high‐latitude South Atlantic waters and in the initiation of North Atlantic Deep Water (NADW) formation. Several model studies have aimed to assess the impacts of DP opening on climate, but most of them focused on surface climate, and only few used realistic Eocene boundary conditions. Here, we revisit the impact of the DP opening on ocean circulation with the IPSL‐CM5A2 Earth System Model. Using appropriate middle Eocene (40 Ma) boundary conditions, we perform and analyze simulations with different depths of the DP (0, 100, 1,000, and 2,500 m) and compare results to existing geochemical data. Our experiments show that DP opening has a strong effect on Eocene ocean structure and dynamics even for shallow depths. The DP opening notably allows the formation of a proto‐ACC and induces deep ocean cooling of 1.5°C to 2.5°C in most of the Southern Hemisphere. There is no NADW formation in our simulations regardless of the depth of the DP, suggesting that the DP on its own is not a primary control of deepwater formation in the North Atlantic. This study elucidates how and to what extent the opening of the DP contributed to the establishment of the modern global thermohaline circulation.