Advances in cosmogenic nuclide exposure dating have made moraines valuable terrestrial recorders of palaeoclimate. A growing number of moraine chronologies reported from the Central Andes show that tropical glaciers responded sensitively to past changes in precipitation and temperature over timescales ranging from 103 to 105 years. However, the causes of past glaciation in the Central Andes remain uncertain. Explanations have invoked insolation-modulated variability in the strength of the South American Summer Monsoon, teleconnections with the North Atlantic Ocean, and/or cooling in the Southern Hemisphere. The driver for these past climate changes is difficult to identify, partly due to a lack of dated moraine records, especially in climatically sensitive areas of the southern Central Andes. Moreover, new constraints are needed on precisely where and when glaciers advanced. We use cosmogenic 10Be produced in situ to determine exposure ages for three generations of moraines at the Sierra de Aconquija, situated at 27°S on the eastern flank of the southern Central Andes. These moraines record glacier advances at approximately 22 ka and 40 ka, coincident with summer insolation maxima in the sub-tropics of the Southern Hemisphere, as well as at 12.5 ka and 13.5 ka during the Younger Dryas and the Antarctic Cold Reversal, respectively. We also identify minor glaciation during Bond Event 5, also known as the 8.2 ka event. These moraines register past climate changes with high fidelity, and currently constitute the southernmost dated record of glaciation on the eastern flank of the Central Andes. To contextualise these results, we compile 10Be data reported from 144 moraines in the eastern Central Andes that represent past glacier advances. We re-calculate exposure ages from these data using an updated reference production rate, and we re-interpret the moraine ages by taking the oldest clustered boulder age (after the exclusion of outliers attributed to nuclide inheritance) as closest to the timing of glacier advance—an approach for which we provide empirical justification. This compilation reveals that Central Andean glaciers have responded to changes in temperature and precipitation. We identify cross-latitude advances in phase with insolation cycles, the last global glacial maximum, and episodes of strengthened monsoonal moisture transport including the Younger Dryas and Heinrich Stadials 1 and 2. Our results from the Sierra de Aconquija allow us to constrain the southerly limit of enhanced precipitation associated with Heinrich Stadials at ∼25°S. More broadly, our findings demonstrate at both local and regional scales that moraines record past climate variability with a fine spatial and temporal resolution.