Compound MHW-OAX events, during which marine heatwaves (MHWs) co-occur with ocean acidity extreme (OAX) events, can have larger impacts on marine ecosystems than the individual extremes. Using monthly open-ocean observations over the period 1982-2019, we show that globally 1.8 in 100 months (or about one out of five present-day MHW months) are compound MHW-OAX event months under a present-day baseline, almost twice as many as expected for 90th percentile extreme event exceedances if MHWs and OAX events were statistically independent. Compound MHW-OAX events are most likely in the subtropics (2.7 in 100 months; 10 degrees-40 degrees latitude) and less likely in the equatorial Pacific and the mid-to-high latitudes (0.7 in 100 months; >40 degrees latitude). The likelihood pattern results from opposing effects of temperature and dissolved inorganic carbon on [H+]. The likelihood is higher where the positive effect on [H+] from increased temperatures during MHWs outweighs the negative effect on [H+] from co-occurring decreases in dissolved inorganic carbon. Daily model output from a large-ensemble simulation of an Earth system model is analyzed to assess changes in the MHW-OAX likelihood under climate change. The projected long-term mean warming and acidification trends have the largest effect on the number of MHW-OAX days per year, increasing it from 12 to 265 days per year at 2 degrees C global warming relative to a fixed pre-industrial baseline. Even when long-term trends are removed, an increase in [H+] variability leads to a 60% increase in the number of MHW-OAX days under 2 degrees C global warming. These projected increases may cause severe impacts on marine ecosystems. Compound extreme events in two or more oceanic ecosystem stressors are increasingly considered as a major concern for marine life. Here the authors present a first global analysis on compound marine heatwave and ocean acidity extreme events, identifying hotspots, drivers, and projecting future changes.