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Abstract Growth of the Andes has been attributed to Cenozoic subduction. Although climatic and tectonic processes have been proposed to be first-order mechanisms, their interaction and respective contributions remain largely unclear. Here, we apply three-dimensional, fully-dynamic subduction models to investigate the effect of trench-axial sediment transport and subduction on Andean growth, a mechanism that involves both climatic and tectonic processes. We find that the thickness of trench-fill sediments, a proxy of plate coupling (with less sediments causing stronger coupling), exerts an important influence on the pattern of crustal shortening along the Andes. The southward migrating Juan Fernandez Ridge acts as a barrier to the northward flowing trench sediments, thus expanding the zone of plate coupling southward through time. Consequently, the predicted history of Andean shortening is consistent with observations. Southward expanding crustal shortening matches the kinematic history of inferred compression. These results demonstrate the importance of climate-tectonic interaction on mountain building.