The Younger Dryas stadial, a cold event spanning 12,800 to 11,500 years ago, during the last deglaciation, is thought to coincide with the last major glacial re-advance in the tropical Andes1. This interpretation relies mainly on cosmic-ray exposure dating of glacial deposits. Recent studies, however, have established new production rates2, 3, 4 for cosmogenic 10Be and 3He, which make it necessary to update all chronologies in this region1, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 and revise our understanding of cryospheric responses to climate variability. Here we present a new 10Be moraine chronology in Colombia showing that glaciers in the northern tropical Andes expanded to a larger extent during the Antarctic cold reversal (14,500 to 12,900 years ago) than during the Younger Dryas. On the basis of a homogenized chronology of all 10Be and 3He moraine ages across the tropical Andes, we show that this behaviour was common to the northern and southern tropical Andes. Transient simulations with a coupled global climate model suggest that the common glacier behaviour was the result of Atlantic meridional overturning circulation variability superimposed on a deglacial increase in the atmospheric carbon dioxide concentration. During the Antarctic cold reversal, glaciers advanced primarily in response to cold sea surface temperatures over much of the Southern Hemisphere. During the Younger Dryas, however, northern tropical Andes glaciers retreated owing to abrupt regional warming in response to reduced precipitation and land–surface feedbacks triggered by a weakened Atlantic meridional overturning circulation. Conversely, glacier retreat during the Younger Dryas in the southern tropical Andes occurred as a result of progressive warming, probably influenced by an increase in atmospheric carbon dioxide. Considered with evidence from mid-latitude Andean glaciers16, our results argue for a common glacier response to cold conditions in the Antarctic cold reversal exceeding that of the Younger Dryas.