Subduction along the western margin of South America has been active since the Jurassic, but Andean orogeny started in the middle Cretaceous and was preceded by backarc extension in the Jurassic-Early Cretaceous. The timing and sequence of these events has remained unexplained. Here I present a four-dimensional buoyancy-driven whole-mantle subduction model implying that the ~200 Myr geological evolution can be attributed to sinking of a wide slab into a layered mantle, where upper-mantle wide-slab subduction causes backarc extension, while whole-mantle (upper+lower) wide-slab subduction drives Andean orogeny. The model reproduces the maximum shortening and crustal thickness observed in the Central Andes and their progressive northward and southward decrease. The subduction evolution coincides with a 29° decrease in slab dip angle, explaining ~200 km of Jurassic-present eastward migration of the Central Andean magmatic arc. Such arc migration negates proposed long-term subduction erosion and continental destruction, but is consistent with long-term crustal growth.