Extreme precipitation and floods in Europe are a recurring natural hazard causing large socioeconomic damages. Here we investigate the connection between annual maxima (AM) daily precipitation at a pan-European scale and atmospheric rivers (ARs), narrow filaments that convey the majority of the poleward water vapor transport within extratropical cyclones. We show that ARs are responsible for many AM precipitation days in Western Europe. The relationship is especially strong along the western European seaboard, with some areas having eight of their top 10 AM related to ARs. The effects of ARs are also seen as far inland as Germany and Poland. Southern Europe was most affected by ARs under negative North Atlantic Oscillation (NAO) conditions, whereas northern Europe was more associated with a positive relationship between ARs and an NAO-type pattern. Our results suggest that ARs are critical in explaining the upper tail of the extreme precipitation distribution in Western Europe.