Compound drought and heatwave (CDHW) events have garnered increased attention due to their significant impacts on agriculture, energy, water resources, and ecosystems. We quantify the projected future shifts in CDHW characteristics (such as frequency, duration, and severity) due to continued anthropogenic warming relative to the baseline recent observed period (1982 to 2019). We combine weekly drought and heatwave information for 26 climate divisions across the globe, employing historical and projected model output from eight Coupled Model Intercomparison Project 6 GCMs and three Shared Socioeconomic Pathways. Statistically significant trends are revealed in the CDHW characteristics for both recent observed and model simulated future period (2020 to 2099). East Africa, North Australia, East North America, Central Asia, Central Europe, and Southeastern South America show the greatest increase in frequency through the late 21st century. The Southern Hemisphere displays a greater projected increase in CDHW occurrence, while the Northern Hemisphere displays a greater increase in CDHW severity. Regional warmings play a significant role in CDHW changes in most regions. These findings have implications for minimizing the impacts of extreme events and developing adaptation and mitigation policies to cope with increased risk on water, energy, and food sectors in critical geographical regions.