The tectonic configuration of the Caribbean plate is defined by inward‐dipping double subduction at its boundaries with the North American and Cocos plates. This geometry resulted from a Paleogene plate reorganization, which involved the abandonment of an older subduction system, the Great Arc of the Caribbean (GAC), and conversion into a transform margin during Lesser Antilles (LA) arc formation. Previous models suggest that a collision between the GAC and the Bahamas platform along the North American passive margin caused this event. However, geological and geophysical constraints from the Greater Antilles do not show a large‐scale compressional episode that should correspond to such a collision. We propose an alternative model for the evolution of the region where lower mantle penetration of the Farallon slab promotes the onset of subduction at the LA. We integrate tectonic constraints with seismic tomography to analyze the timing and dynamics of the reorganization, showing that the onset of LA subduction corresponds to the timing of Farallon/Cocos slab penetration. With numerical subduction models, we explore whether slab penetration constitutes a dynamically feasible set of mechanisms to initiate subduction in the overriding plate. In our models, when the first slab (Farallon/Cocos) enters the lower mantle, compressive stresses increase at the eastern margin of the upper plate, and a second subduction zone (LA) is initiated. The resulting first‐order slab geometries, timings, and kinematics compare well with plate reconstructions. More generally, similar slab dynamics may provide a mechanism not only for the Caribbean reorganization but also for other tectonic episodes throughout the Americas.