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Speleothem oxygen isotope records (δ18O) of tropical South American rainfall in the late Quaternary show a zonal "South American Precipitation Dipole" (SAPD). The dipole is characterized by opposing east‐west precipitation anomalies compared to the present—wetter in the east and drier in the west at the mid‐Holocene (∼7 ka), and drier in the east and wetter in the west at the Last Glacial Maximum (∼21 ka). However, the SAPD remains enigmatic because it is expressed differently in western versus eastern δ18O records and isotope‐enabled climate model simulations usually misrepresent the magnitude and/or spatial pattern of δ18O change. Here, we address the SAPD enigma in two parts. First, we re‐interpret the δ18O data to account for upwind rainout effects that are known to be pervasive in tropical South America, but are not always considered in Quaternary paleoclimate studies. Our revised interpretation reconciles the δ18O data with cave infiltration and other proxy records, and indicates that the centroid of tropical South American rainfall has migrated zonally over time. Second, using an energy balance model of tropical atmospheric circulation, we hypothesize that zonal migration of the precipitation centroid can be explained by regional energy budget shifts, such as changing Saharan albedo associated with the African Humid Period, that have not been modeled in previous SAPD studies. This hypothesis of a migrating precipitation centroid presents a new framework for interpreting δ18O records from tropical South America and may help explain the zonal rainfall anomalies that predate the late Quaternary. Plain Language Summary: Paleoclimate data suggest that, in the last ∼25,000 years, tropical South American precipitation has changed substantially, but in opposite directions between the east and west. This opposing east‐west pattern in past rainfall is known as the "South American Precipitation Dipole," and its end‐member states approximately coincide with the Last Glacial Maximum (∼21,000 years ago) and mid‐Holocene (∼7,000 years ago), respectively. However, the cause of the dipole is debated because different models produce different results, and the interpretations of data are in conflict. Central in this conflict are oxygen isotope tracers of past precipitation which show different trends over space. We present a new interpretation of these data, backed by model results, which suggests that the dipole is driven by the centroid, or focus, of tropical South American precipitation migrating from west‐to‐east (and back) across tropical South America. We test this precipitation centroid migration hypothesis with an energy balance climate model which reproduces the expected east‐west differences for the Last Glacial Maximum and mid‐Holocene. The precipitation centroid migration hypothesis is a possible solution to the precipitation dipole enigma, but it remains to be tested in more sophisticated climate models. Key Points: The late Quaternary South American Precipitation Dipole drives opposing east‐west precipitation anomalies in tropical South AmericaDipole transitions can drive changes in rainfall greater than 1,000 mm/yrSpatial migration of the precipitation centroid can explain dipole transitions and reconcile proxy‐model conflicts [ABSTRACT FROM AUTHOR]