Atmospheric rivers (ARs) are key agents of poleward heat and moisture transport, yet the extent to which tropical moisture directly feeds AR precipitation at higher latitudes remains debated. Here we present a forty-year global climatology of moisture sources for AR-related precipitation, combining deep learning-based AR detection with Lagrangian moisture tracking. We reveal that AR precipitation worldwide organizes into two coherent and contrasting moisture transport regimes. Along western continental boundaries, AR precipitation is predominantly sustained by extratropical moisture convergence, with tropical contributions typically limited to 30–40%, whereas eastern boundaries exhibit shorter transport pathways with substantially larger tropical contributions, averaging 60–70%. These persistent west–east asymmetries reflect systematic shifts in moisture origin as ARs evolve from early subtropical acquisition to mature extratropical transport. We further show a strong negative correlation between tropical contribution and latitude, demonstrating that direct tropical moisture delivery is not a requirement for AR precipitation at high latitudes. Instead, tropical moisture primarily preconditions AR formation, while the water mass that ultimately precipitates is progressively replaced along the poleward pathway. Taken together, our findings reconcile divergent assessments of tropical moisture influence on AR precipitation and thus deepen our understanding of how Earth’s hydrological engine redistributes atmospheric water across the planet.