Reported COVID-19 cases and deaths provide a delayed and incomplete picture of SARS-CoV-2 infections in the United States (US). Accurate estimates of both the timing and magnitude of infections are needed to characterize viral transmission dynamics and better understand COVID-19 disease burden. We estimated time trends in SARS-CoV-2 transmission and other COVID-19 outcomes for every county in the US, from the first reported COVID-19 case in January 13, 2020 through January 1, 2021. To do so we employed a Bayesian modeling approach that explicitly accounts for reporting delays and variation in case ascertainment, and generates daily estimates of incident SARS-CoV-2 infections on the basis of reported COVID-19 cases and deaths. The model is freely available as the covidestim R package. Nationally, we estimated there had been 49 million symptomatic COVID-19 cases and 404,214 COVID-19 deaths by the end of 2020, and that 28% of the US population had been infected. There was county-level variability in the timing and magnitude of incidence, with local epidemiological trends differing substantially from state or regional averages, leading to large differences in the estimated proportion of the population infected by the end of 2020. Our estimates of true COVID-19 related deaths are consistent with independent estimates of excess mortality, and our estimated trends in cumulative incidence of SARS-CoV-2 infection are consistent with trends in seroprevalence estimates from available antibody testing studies. Reconstructing the underlying incidence of SARS-CoV-2 infections across US counties allows for a more granular understanding of disease trends and the potential impact of epidemiological drivers.