The Euromediterranean area is a key region in which the link between atmospheric moisture transport and hydrometeorological extremes concerns. Atmospheric rivers, the main moisture transport mechanism affecting the region, play a notable role in extreme precipitation there. Moreover, moisture transport deficits from two of the major oceanic moisture sources of the planet, the North Atlantic Ocean and the Mediterranean Sea, are strongly related to drought occurrence in that region. Here, we examine the projected changes in these relationships with global warming, under a high-emission scenario (shared socioeconomic pathway 5–8.5). Here we show that, for the mid-21st century, a moderate increase in the influence of moisture transport on winter precipitation maxima is projected, in line with its increasing concurrence with atmospheric rivers. A stronger increase is estimated for the relationship between moisture transport deficits and drought occurrence, for which probabilities between two and three times greater than those observed in the present climate are obtained for the mid- and end-21st century. This highlights the increasing importance of moisture transport from the ocean in future droughts in the region, especially in the context of reduced local moisture inputs from terrestrial evaporation as a consequence of drier soil.