Songbirds (oscine passerines) are the most species rich and cosmopolitan bird group, comprising almost half of global avian species diversity. Because of their diversity and ubiquity, songbirds are used extensively in studies of evolutionary ecology, diversification, and ethology. Songbirds originated in Australia, but the evolutionary trajectory from a single species in an isolated continent to worldwide proliferation is poorly understood. Prior research suggested songbird diversification scenarios that are largely uncoupled from Earth history, including extensive diversification of lineages in New Guinea prior to its emergence as a landmass and long-distance dispersal to Africa or Asia when no dispersal corridors existed. However, these results may be flawed because the studies relied on unresolved phylogenetic relationships and a controversial biogeographic time calibration. Here, we combine the first genome-scale DNA sequence data set for songbirds, fossil-based time calibrations, and geologically informed biogeographic reconstructions to provide the first well-supported evolutionary hypothesis for the group. We show that songbird diversification began in the Oligocene, but accelerated in the early Miocene, at approximately half the age of most previous estimates. This burst of diversification occurred after island formation in Wallacea, which provided the first dispersal corridor out of Australia, and resulted in independent waves of songbird expansion through Asia to the rest of the globe. Although New Guinea presently contains high songbird species richness, our data unambiguously falsify the proto-Papuan hypothesis for early songbird diversification and suggest that New Guinea has, instead, served as an “evolutionary refuge” for Australian lineages that have diversified more recently within the island. Our results reconcile songbird evolution with Earth history and link a major radiation of terrestrial biodiversity to early diversification within an isolated Australian continent.