Indian Ocean circulation affects marine life and global climate through important oceanic teleconnections with the Pacific, South Atlantic and Southern Ocean. Based on 28 Coupled Model Intercomparison Project Phase 5 (CMIP5) models, this study finds that many aspects of the South Indian Ocean circulation slow significantly with increased greenhouse gas emissions. Off the west coast of Australia, the models project a consistent weakening of the poleward flowing Leeuwin Current and equatorward flowing Leeuwin Undercurrent. These changes are linked to a reduction in downwelling between these currents and the zonal geostrophic transport that feeds the Leeuwin Current. We find that projected intermodel differences in the zonal flows is related to the meridional pressure gradient along the west coast of Australia. While both the Indonesian Throughflow and the meridional pressure gradient are projected to weaken, there is no intermodel relationship between these changes. Additionally, the local southerlies are projected to intensify, which might be expected to weaken the Leeuwin Current, however, again we find no intermodel relationship between Leeuwin Current strength and meridional wind stress. In the southwest Indian Ocean, the models project a robust weakening of the poleward flowing East Madagascar Current, Mozambique Channel and Agulhas Current. These changes are compensated by a small reduction of upper-ocean transport, reduced Indonesian Throughflow transport and a substantial reduction of deep ocean transport entering the Indian Ocean from the south.