The American tropics (the Neotropics) are the most species-rich realm on Earth, and for centuries, scientists have attempted to understand the origins and evolution of their biodiversity. It is now clear that different regions and taxonomic groups have responded differently to geological and climatic changes. However, we still lack a basic understanding of how Neotropical biodiversity was assembled over evolutionary timescales. Here we infer the timing and origin of the living biota in all major Neotropical regions by performing a cross-taxonomic biogeographic analysis based on 4,450 species from six major clades across the tree of life (angiosperms, birds, ferns, frogs, mammals, and squamates), and integrate >1.3 million species occurrences with large-scale phylogenies. We report an unprecedented level of biotic interchange among all Neotropical regions, totaling 4,525 dispersal events. About half of these events involved transitions between major environmental types, with a predominant directionality from forested to open biomes. For all taxonomic groups surveyed here, Amazonia is the primary source of Neotropical diversity, providing >2,800 lineages to other regions. Most of these dispersal events were to Mesoamerica (∼1,500 lineages), followed by dispersals into open regions of northern South America and the Cerrado and Chaco biomes. Biotic interchange has taken place for >60 million years and generally increased toward the present. The total amount of time lineages spend in a region appears to be the strongest predictor of migration events. These results demonstrate the complex origin of tropical ecosystems and the key role of biotic interchange for the assembly of regional biotas.