COVID-19 disease caused by the SARS-CoV-2 virus is characterized by dysregulation of effector T cells and accumulation of exhausted T cells. T cell responses to viruses can be corrected by adoptive cellular therapy using donor-derived virus-specific T cells. One approach is the establishment of banks of HLA-typed virus-specific T cells for rapid deployment to patients. Here we show that SARS-CoV-2-exposed blood donations contain CD4 and CD8 memory T cells which recognize SARS-CoV-2 spike, nucleocapsid and membrane antigens. Peptides of these antigens can be used to isolate virus-specific T cells in a GMP-compliant process. The isolated T cells can be rapidly expanded using GMP-compliant reagents for use as an allogeneic therapy. Memory and effector phenotypes are present in the selected virus-specific T cells, but our method rapidly expands the desirable central memory phenotype. A manufacturing yield ranging from 10 to 10 T cells can be obtained within 21 days culture. Thus, multiple therapeutic doses of virus-specific T cells can be rapidly generated from convalescent donors for potential treatment of COVID-19 patients.