The explosive development of extratropical cyclones and atmospheric rivers plays a crucial role in driving extreme weather in the mid-latitudes, such as compound windstorm-flood events. Although both explosive cyclones and atmospheric rivers are well understood and their relationship has been studied previously, there is still a gap in our understanding of how a warmer climate may affect their concurrence. Here, we focus on evaluating the current climatology and assessing changes in the future concurrence between atmospheric rivers and explosive cyclones in the North Atlantic. To accomplish this, we independently detect and track atmospheric rivers and extratropical cyclones and study their concurrence in both ERA5 reanalysis and CMIP6 historical and future climate simulations. In agreement with the literature, atmospheric rivers are more often detected in the vicinity of explosive cyclones than non-explosive cyclones in all datasets, and the atmospheric river intensity increases in all the future scenarios analysed. Furthermore, we find that explosive cyclones associated with atmospheric rivers tend to be longer lasting and deeper than those without. Notably, we identify a significant and systematic future increase in the cyclones and atmospheric river concurrences. Finally, under the high-emission scenario, the explosive cyclone and atmospheric river concurrences show an increase and model agreement over western Europe. As such, our work provides a novel statistical relation between explosive cyclones and atmospheric rivers in CMIP6 climate projections and a characterization of their joint changes in intensity and location.