The southern westerly wind belt (SWW) interacts with the Antarctic Circumpolar Current and strongly impacts the Southern Ocean carbon budget, and Antarctic ice-sheet dynamics across glacial-interglacial cycles. We investigated precipitation-driven sediment input changes to the Southeast Pacific off the southern margin of the Atacama Desert over the past one million years, revealing strong precession (19/23-ka) cycles. Our simulations with 2 ocean-atmosphere general circulation models suggest that observed cyclic rainfall changes are linked to meridional shifts in water vapor transport from the tropical Pacific toward the southern Atacama Desert. These changes reflect a precessional modulation of the split in the austral winter South Pacific jet stream. For precession maxima, we infer significantly enhanced rainfall in the southern Atacama Desert due to a stronger South Pacific split jet with enhanced subtropical/subpolar jets, and a weaker midlatitude jet. Conversely, we derive dry conditions in northern Chile related to reduced subtropical/subpolar jets and an enhanced midlatitude jet for precession minima. The presence of precessional cycles in the Pacific SWW, and lack thereof in other basins, indicate that orbital-scale changes of the SWW were not zonally homogeneous across the Southern Hemisphere, in contrast to the hemispherewide shifts of the SWW suggested for glacial terminations. The strengthening of the jet is unique to the South Pacific realm and might have affected winter-controlled changes in the mixed layer depth, the formation of intermediate water, and the buildup of sea-ice around Antarctica, with implications for the global overturning circulation and the oceanic storage of atmospheric CO2.