As global compound drought and heatwave (CDHW) events have shown a trend towards multi-regional concurrency, quantifying their synchronous structures and exploring potential drivers for synchronizing CDHW events are crucial for disaster prevention and mitigation. This study identifies global CDHW events based on daily soil moisture and maximum temperature during 1979–2022, and investigates the topological characteristics of concurrent CDHW events through complex network (CN) analysis. Subsequently, the potential physical drivers causing the spatial concurrence of CDHW events are explored based on their synchronous structures. Results show that high-incidence regions for CDHW events include eastern North America, northern and southeastern South America, northern Eurasia, Southeast Asia and the central Yangtze River Basin. The CN coefficients derived from the synchronization network unveil a highly heterogeneous connectivity structure underlying global CDHW events. In northern and southeastern South America, synchronous CDHW events primarily occur at a regional scale. In contrast, regions such as the Amazon, the Congo Basin and the Yangtze River Basin, which serve as important hubs within the synchronization network, can synchronize CDHW events with other hubs at an inter-continental or even inter-hemispheric scale. Hubs at high latitudes in the Northern Hemisphere predominantly synchronize CDHW events with remote places at similar latitudes. Furthermore, the simultaneous occurrences of CDHW events in western North America, western Russia and the Yangtze River Basin are strongly associated with sea surface temperature anomalies in the central Pacific, North Pacific, North Atlantic, and Barents Sea, while the synchronous CDHW event onsets across multiple regions in the middle and high latitudes of the Northern Hemisphere are closely relevant to Rossby waves. These insights are valuable for proposing adaptation measures for spatially synchronous CDHW events and predicting such events in the future.