High frequency screening of populations has been proposed as a strategy in facilitating control of the COVID-19 pandemic. We use computational modeling, coupled with clinical data from rapid antigen tests, to predict the impact of frequent viral antigen rapid testing on COVID-19 spread and outcomes. Using patient nasal or nasopharyngeal swab specimens, we demonstrate that the sensitivity/specificity of two rapid antigen tests compared to quantitative real-time polymerase chain reaction (qRT-PCR) are 80.0%/91.1% and 84.7%/85.7%, respectively; moreover, sensitivity correlates directly with viral load. Based on COVID-19 data from three regions in the United States and São José do Rio Preto, Brazil, we show that high frequency, strategic population-wide rapid testing, even at varied accuracy levels, diminishes COVID-19 infections, hospitalizations, and deaths at a fraction of the cost of nucleic acid detection via qRT-PCR. We propose large-scale antigen-based surveillance as a viable strategy to control SARS-CoV-2 spread and to enable societal re-opening.