Background: Previous studies on the epidemiology and clinical characteristics of COVID-19 have generally been limited to hospitalized patients. The aim of this study was to describe the complete clinical spectrum of COVID-19, based on a nationwide cohort with extensive diagnostic testing and a rigorous contact tracing approach. Methods: A population-based cohort study examining symptom progression using prospectively recorded data on all individuals with a positive test (RT-PCR) for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) who were enrolled in a telehealth monitoring service provided to all identified cases in Iceland. Symptoms were systematically monitored from diagnosis to recovery. Results: From January 31 to April 30, 2020, a total of 45,105 individuals (12% of the Icelandic population) were tested for SARS-CoV-2, of whom 1797 were positive, yielding a population incidence of 5 per 1000 individuals. The most common presenting symptoms were myalgia (55%), headache (51%), and non-productive cough (49%). At the time of diagnosis, 5.3% of cases reported no symptoms and 3.1% remained asymptomatic during follow-up. In addition, 216 patients (13.8%) and 349 patients (22.3%) did not meet the case definition of the Centers for Disease Control and Prevention and the World Health Organization, respectively. The majority (67.5%) of patients had mild symptoms throughout the course of the disease. Conclusion: In the setting of broad access to diagnostic testing, the majority of SARS-CoV-2-positive patients were found to have mild symptoms. Fever and dyspnea were less common than previously reported. A substantial proportion of patients did not meet recommended case definitions at the time of diagnosis.