Understanding the hallmarks of the immune response to SARS-CoV-2 is critical for fighting the COVID-19 pandemic. We assessed antibody and T cell reactivity in convalescent COVID-19 patients and healthy donors sampled both prior to and during the pandemic. Healthy donors examined during the pandemic exhibited increased numbers of SARS-CoV-2-specific T cells, but no humoral response. Their probable exposure to the virus resulted in either asymptomatic infection without antibody secretion or activation of preexisting immunity. In convalescent patients, we observed a public and diverse T cell response to SARS-CoV-2 epitopes, revealing T cell receptor (TCR) motifs with germline-encoded features. Bulk CD4 and CD8 T cell responses to the spike protein were mediated by groups of homologous TCRs, some of them shared across multiple donors. Overall, our results demonstrate that the T cell response to SARS-CoV-2, including the identified set of TCRs, can serve as a useful biomarker for surveying antiviral immunity.