The southern Central Andes (29°S-39°S) is a key area to better understand the mechanisms of non-collisional mountain building associated with changes in oceanic plate dip geometry and the interaction between the oceanic and continental plates. The orogen experienced an increase of shortening during the last 35 Ma which is coeval with the southward migration of a flat subduction segment and the passage of a bathymetric anomaly known as the Juan Fernandez Ridge. Based on data-driven geodynamic numerical modelling, we use the present-day plate configuration to assess the role of the flat-slab on the deformation of the overriding plate. The resulting deformation field suggests that the shallowing of the oceanic slab controlled the onset of the compression at ~10 Ma before the arrival of the ridge leading to the formation of a ~370-km-wide transpressive shear zone at the transition between the flat (27°S - 32°S) and the steep slab segments (south of 33°S). The contraction of the crust is accommodated by the dextral rotation of micro-crustal Sierras Pampeanas basement blocks and strike-slip deformation at their borders (i.e., thick-skin foreland deformation). We propose a novel concept for oceanic and continental plate interaction, where the southward migration of the flat slab functions as a conveyor belt for upper-plate crustal deformation, with an increase in the intensity of deformation foreshadowing the flat-slab arrival.