Alongside mean increases in poleward moisture transport (PMT) to the Arctic, most climate models also project a linear increase in the interannual variability (IAV) with future warming. It is still uncertain to what extent atmospheric rivers (ARs) contribute to both the mean and the IAV increase of PMT. We analyzed large-ensemble climate simulations to 1) explore the link between PMT and ARs in the present-day (PD) and in two warmer climates (+2°C and +3°C compared to pre-industrial global mean temperature), 2) assess the dynamic contribution to changes in future ARs, and 3) analyze the effect of ARs on Arctic climate on interannual timescales. We find that the share of AR-related PMT (ARPMT) to PMT increases from 42% in the PD to 53% in the +3°C climate. The increase in AR-frequency and intensity is almost exclusively caused by significantly higher atmospheric moisture levels, while dynamic changes can regionally amplify or dampen the moisture-induced increase in ARs. The amount of ARs reaching the Arctic in any given region and season strongly depends on the regional jet stream position and speed southwest of this region. Our results indicate that positive ARPMT anomalies are profoundly linked to increased surface air temperature and precipitation, especially in the colder seasons, and have a predominantly negative effect on sea ice. AR events are expected to strongly affect Arctic climate variability in the future, when any AR-induced temperature anomaly occurs in an already warmer Arctic and a larger share of precipitation falls as rain.