In January 2020, a novel betacoronavirus (family Coronaviridae), named severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), was identified as the etiological agent of a cluster of pneumonia cases occurring in Wuhan City, Hubei Province, China1,2. The disease arising from SARS-CoV-2 infection, coronavirus disease 2019 (COVID-19), subsequently spread rapidly causing a worldwide pandemic. Here we examine the added value of near real-time genome sequencing of SARS-CoV-2 in a subpopulation of infected patients during the first 10 weeks of COVID-19 containment in Australia and compare findings from genomic surveillance with predictions of a computational agent-based model (ABM). Using the Australian census data, the ABM generates over 24 million software agents representing the population of Australia, each with demographic attributes of an anonymous individual. It then simulates transmission of the disease over time, spreading from specific infection sources, using contact rates of individuals within different social contexts. We report that the prospective sequencing of SARS-CoV-2 clarified the probable source of infection in cases where epidemiological links could not be determined, significantly decreased the proportion of COVID-19 cases with contentious links, documented genomically similar cases associated with concurrent transmission in several institutions and identified previously unsuspected links. Only a quarter of sequenced cases appeared to be locally acquired and were concordant with predictions from the ABM. These high-resolution genomic data are crucial to track cases with locally acquired COVID-19 and for timely recognition of independent importations once border restrictions are lifted and trade and travel resume.