A range of solar radiation management (SRM) techniques has been proposed to counter anthropogenic climate change. Here, we examine the potential effects of stratospheric sulfate aerosols and solar insolation reduction on tropospheric ozone and ozone at Earth's surface. Ozone is a key air pollutant, which can produce respiratory diseases and crop damage. Using a version of the Community Earth System Model from the National Center for Atmospheric Research that includes comprehensive tropospheric and stratospheric chemistry, we model both stratospheric sulfur injection and solar irradiance reduction schemes, with the aim of achieving equal levels of surface cooling relative to the Representative Concentration Pathway 6.0 scenario. This allows us to compare the impacts of sulfate aerosols and solar dimming on atmospheric ozone concentrations. Despite nearly identical global mean surface temperatures for the two SRM approaches, solar insolation reduction increases global average surface ozone concentrations, while sulfate injection decreases it. A fundamental difference between the two geoengineering schemes is the importance of heterogeneous reactions in the photochemical ozone balance with larger stratospheric sulfate abundance, resulting in increased ozone depletion in mid-A nd high latitudes. This reduces the net transport of stratospheric ozone into the troposphere and thus is a key driver of the overall decrease in surface ozone. At the same time, the change in stratospheric ozone alters the tropospheric photochemical environment due to enhanced ultraviolet radiation. A shared factor among both SRM scenarios is decreased chemical ozone loss due to reduced tropospheric humidity. Under insolation reduction, this is the dominant factor giving rise to the global surface ozone increase. Regionally, both surface ozone increases and decreases are found for both scenarios; that is, SRM would affect regions of the world differently in terms of air pollution. In conclusion, surface ozone and tropospheric chemistry would likely be affected by SRM, but the overall effect is strongly dependent on the SRM scheme. Due to the health and economic impacts of surface ozone, all these impacts should be taken into account in evaluations of possible consequences of SRM.