Accurate and timely detection of recombinant lineages is crucial for interpreting genetic variation, reconstructing epidemic spread, identifying selection and variants of interest, and accurately performing phylogenetic analyses. During the SARS-CoV-2 pandemic, genomic data generation has exceeded the capacities of existing analysis platforms, thereby crippling real-time analysis of viral recombination. Low SARS-CoV-2 mutation rates make detecting recombination difficult. Here, we develop and apply a novel phylogenomic method to exhaustively search a nearly comprehensive SARS-CoV-2 phylogeny for recombinant lineages. We investigate a 1.6M sample tree, and identify 606 recombination events. Approximately 2.7% of sequenced SARS-CoV-2 genomes have recombinant ancestry. Recombination breakpoints occur disproportionately in the Spike protein region. Our method empowers comprehensive real time tracking of viral recombination during the SARS-CoV-2 pandemic and beyond.