The building of the Andes results from the subduction of the oceanic Nazca plate underneath the South American continent. However, how and why the Andes and their curvature, the Bolivian orocline, formed in the Cenozoic era (65.5million years (Myr) ago to present), despite subduction continuing since the Mesozoic era (251.0-65.5Myr ago), is still unknown. Three-dimensional numerical subduction models demonstrate that variations in slab thickness, arising from the Nazca plate's age at the trench, produce a cordilleran morphology consistent with that observed. The age-dependent sinking of the slab in the mantle drives traction towards the trench at the base of the upper plate, causing it to thicken. Thus, subducting older Nazca plate below the Central Andes can explain the locally thickened crust and higher elevations. Here we demonstrate that resultant thickening of the South American plate modifies both shear force gradients and migration rates along the trench to produce a concave margin that matches the Bolivian orocline. Additionally, the varying forcing along the margin allows stress belts to form in the upper-plate interior, explaining the widening of the Central Andes and the different tectonic styles found on their margins, the Eastern and Western Cordilleras. The rise of the Central Andes and orocline formation are directly related to the local increase of Nazca plate age and an age distribution along the margin similar to that found today; the onset of these conditions only occurred in the Eocene epoch. This may explain the enigmatic delay of the Andean orogeny, that is, the formation of the modern Andes.