The Coral Triangle (CT) region of the Indo-Pacific realm harbors an extraordinary number of species, with richness decreasing away from this biodiversity hotspot. Despite multiple competing hypotheses, the dynamics underlying this regional diversity pattern remain poorly understood. Here, we use a time-calibrated evolutionary tree of living reef coral species, their current geographic ranges, and model-based estimates of regional rates of speciation, extinction, and geographic range shifts to show that origination rates within the CT are lower than in surrounding regions, a result inconsistent with the long-standing center of origin hypothesis. Furthermore, endemism of coral species in the CT is low, and the CT endemics are older than relatives found outside this region. Overall, our model results suggest that the high diversity of reef corals in the CT is largely due to range expansions into this region of species that evolved elsewhere. These findings strongly support the notion that geographic range shifts play a critical role in generating species diversity gradients. They also show that preserving the processes that gave rise to the striking diversity of corals in the CT requires protecting not just reefs within the hotspot, but also those in the surrounding areas.