Compound drought and heatwave (CDHW) events have garnered much attention in recent studies. However, thus far, the identification of such events is oversimplified, and their association with natural climate variability is not fully explored. Here, we derive anomalies in the weekly self‐calibrated Palmer Drought Severity Index (sc_PDSI) and daily maximum temperatures to identify CDHW events from 1982 to 2016 over 26 climate regions across the globe. Using a Poisson Generalized Linear Model (GLM), we analyze yearly occurrences of seasonal CDHW events and their association with the warm and cold phases of El Nino Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), and North Atlantic Oscillation (NAO). ENSO exhibits robust association with CDHW events over the Southern Hemisphere during the austral summer and fall, while PDO influences their occurrences over the Western North America in the Northern Hemisphere during the boreal summer, which is supported by the composites of anomalies in the atmospheric circulations and surface energy budget. However, NAO association with CDHW events is relatively weak. The CDHW occurrence over other regions is driven by a combination of these large‐scale natural forcing. Our analyses also highlight that the cooccurrence of weekly to submonthly scale anomalies in the observed temperature and precipitation may not be always aligned between the observations and the reanalysis. Therefore, caution must be exercised while explaining such observed anomalies on the basis of reanalysis‐based circulations and surface energy budget. Overall, our analyses provide a new insight towards concurrent extremes and should help foster research efforts in this area.