Amazonia is extremely biodiverse, but the mechanisms for the origin of this diversity are still under debate. We propose a diversification model for Amazonia based on the interplay of intrinsic clade functional traits, habitat associations and past geological events, using as a model group the species-rich Neotropical family Marantaceae. Our results show that the species richness of the lineage is predicted by functional strategy, rather than clade age, and thus the fast vs. slow growth functional trade-off is a major determinant of clade diversification in Marantaceae. Rapidly growing clades were mostly associated with highly productive habitats, and their origin and diversification dynamics matched the expansion of fertile soils mediated by Andean uplift c. 23 Mya. Fast-growth strategies probably led to fast molecular evolution, speeding up speciation rates and species accumulation, resulting in higher numbers of extant species. Our results indicate that pure allopatric-dispersal models disconnected from past geological and ecological forces may be inadequate for explaining the evolutionary and diversity patterns in Amazonian lowlands. We suggest that a coupling of the functional trait-niche framework with diversification dynamics provides insights into the evolutionary history of tropical forests and helps elucidate the mechanisms underlying the origin and evolution of its spectacular biodiversity.