Under climate change driven by increased carbon dioxide (CO2) concentrations, stratospheric ozone will respond to temperature and circulation changes, leading to chemistry-climate feedback by modulating large-scale atmospheric circulation and Earth's energy budget. However, there is significant model uncertainty since many processes are involved and few models have a detailed chemistry scheme. This work employs the latest data from Coupled Model Intercomparison Project Phase 6 (CMIP6) to investigate the ozone response to increased CO2. We find that in most models, ozone increases in the upper stratosphere (US) and extratropical lower stratosphere (LS) and decreases in the tropical LS; thus, the total column ozone (TCO) response is small in the tropics. The ozone response is mainly driven by slower chemical destruction cycles in the US and enhanced upwelling in the LS, with a highly model-dependent Arctic ozone response to polar vortex strength changes. We then explore the ozone-climate feedback by combining offline calculations and comparisons between models with ("chem") and without ("no-chem") interactive chemistry. We find that the stratospheric temperature response is substantial, with a global negative radiative forcing ranging from -0.03 to -0.19 Wm-2. We find that chem models consistently simulate less tropospheric warming and a stronger weakening of the polar stratospheric vortex, which result in a larger increase in sudden stratospheric warming (SSW) frequency than in most no-chem models. Our findings show that ozone-climate feedback is essential for the climate system and should be considered in the development of Earth system models.