Climate change has the potential to increase surface ozone (O3) concentrations, known as the "ozone-climate penalty", through changes to atmospheric chemistry, transport and dry deposition. In the tropics, the response of surface O3 to changing climate is relatively understudied but has important consequences for air pollution and human and ecosystem health. In this study, we evaluate the change in surface O3 due to climate change over South America and Africa using three state-of-the-art Earth system models that follow the Shared Socioeconomic Pathway 3-7.0 emission scenario from CMIP6. In order to quantify changes due to climate change alone, we evaluate the difference between simulations including climate change and simulations with a fixed present-day climate. We find that by 2100, models predict an ozone-climate penalty in areas where O3 is already predicted to be high due to the impacts of precursor emissions, namely urban and biomass burning areas, although on average, models predict a decrease in surface O3 due to climate change. We identify a small but robust positive trend in annual mean surface O3 over polluted areas. Additionally, during biomass burning seasons, seasonal mean O3 concentrations increase by 15 ppb (model range 12 to 18 ppb) in areas with substantial biomass burning such as the arc of deforestation in the Amazon. The ozone-climate penalty in polluted areas is shown to be driven by an increased rate of O3 chemical production, which is strongly influenced by NOx concentrations and is therefore specific to the emission pathway chosen. Multiple linear regression finds the change in NOx concentration to be a strong predictor of the change in O3 production, whereas increased isoprene emission rate is positively correlated with increased O3 destruction, suggesting NOx-limited conditions over the majority of tropical Africa and South America. However, models disagree on the role of climate change in remote, low-NOx regions, partly because of significant differences in NOx concentrations produced by each model. We also find that the magnitude and location of the ozone-climate penalty in the Congo Basin has greater inter-model variation than that in the Amazon, so further model development and validation are needed to constrain the response in central Africa. We conclude that if the climate were to change according to the emission scenario used here, models predict that forested areas in biomass burning locations and urban populations will be at increasing risk of high O3 exposure, irrespective of any direct impacts on O3 via the prescribed emission scenario.