The evolution of tropospheric ozone from 1850 to 2100 has been studied using data from Phase 6 of the Coupled Model Intercomparison Project (CMIP6). We evaluate long-term changes using coupled atmosphere–ocean chemistry–climate models, focusing on the CMIP Historical and ScenarioMIP ssp370 experiments, for which detailed tropospheric-ozone diagnostics were archived. The model ensemble has been evaluated against a suite of surface, sonde and satellite observations of the past several decades and found to reproduce well the salient spatial, seasonal and decadal variability and trends. The multi-model mean tropospheric-ozone burden increases from 247 ± 36 Tg in 1850 to a mean value of 356 ± 31 Tg for the period 2005–2014, an increase of 44 %. Modelled present-day values agree well with previous determinations (ACCENT: 336 ± 27 Tg; Atmospheric Chemistry and Climate Model Intercomparison Project, ACCMIP: 337 ± 23 Tg; Tropospheric Ozone Assessment Report, TOAR: 340 ± 34 Tg). In the ssp370 experiments, the ozone burden increases to 416 ± 35 Tg by 2100. The ozone budget has been examined over the same period using lumped ozone production (PO3) and loss (LO3) diagnostics. Both ozone production and chemical loss terms increase steadily over the period 1850 to 2100, with net chemical production (PO3-LO3) reaching a maximum around the year 2000. The residual term, which contains contributions from stratosphere–troposphere transport reaches a minimum around the same time before recovering in the 21st century, while dry deposition increases steadily over the period 1850–2100. Differences between the model residual terms are explained in terms of variation in tropopause height and stratospheric ozone burden.