GPS data suggest that the NW South America corner forms a semi‐rigid block drifting NE‐ward along the regional dextral strike‐slip faults that bound an oceanic terrane accreted in Late Cretaceous times to W Ecuador and Colombia. However, the relevance of both strike‐slip versus thrust tectonics during Cenozoic times and their relation with oceanic terrane accretion are unclear. Here we report on the paleomagnetism of 31 mid‐upper Eocene to upper Miocene mainly volcanic sites from the Cordilleras Occidental and Real of southern Ecuador. Eleven sites show that the western Cordillera Occidental underwent a 24° ± 10° clockwise (CW) rotation with respect to South America after late Miocene times, while no rotation occurred further east. We relate the regional CW rotation to the emplacement of the Cordillera Occidental nappe onto the continental sediments of the Interandean Valley, blanketing the Cordillera's eastern margin. As rotation and continental sedimentation onset ages are similar, we interpret such tectonic depression as a narrow flexural basin formed ahead of the advancing nappe front. The 20°–30° CW Neogene rotation of the Cordillera Occidental is indistinguishable from the post‐Cretaceous rotation of the Coastal forearc oceanic blocks, implying that the whole W Ecuador Andean chain was detached and rotated over a mid‐crustal detachment during the last 10 Ma. Eocene‐Miocene paleomagnetic inclination values are systematically consistent with those expected for South America, thus excluding latitudinal terrane drift. We suggest that the Andes of Ecuador and Peru form the “Ecuadorian Orocline”, formed by opposing orogenic rotations around the Amazonian craton indenter. Key Points 20°–30°CW post‐Late Miocene rotation of the Cordillera Occidental, no rotation of the Cordillera Real, southern Ecuador The southern Cordillera Occidental emplaced as a rotational nappe after the late Miocene‐Pliocene over the flexural Interandean Valley basin No paleomagnetic evidence for latitudinal terrane drift and orogen‐parallel strike‐slip activity since Mid‐Late Eocene (∼40 Ma)