The Alpha, Beta, and Gamma SARS-CoV-2 variants of concern (VOCs) co-circulated globally during 2020 and 2021, fueling waves of infections. They were displaced by Delta during a third wave worldwide in 2021, which, in turn, was displaced by Omicron in late 2021. In this study, we use phylogenetic and phylogeographic methods to reconstruct the dispersal patterns of VOCs worldwide. We find that source-sink dynamics varied substantially by VOC and identify countries that acted as global and regional hubs of dissemination. We demonstrate the declining role of presumed origin countries of VOCs in their global dispersal, estimating that India contributed <15% of Delta exports and South Africa <1%-2% of Omicron dispersal. We estimate that >80 countries had received introductions of Omicron within 100 days of its emergence, associated with accelerated passenger air travel and higher transmissibility. Our study highlights the rapid dispersal of highly transmissible variants, with implications for genomic surveillance along the hierarchical airline network.