Adoptive T-cell immunotherapy has provided promising results in the treatment of viral complications in humans, particularly in the context of immunocompromised patients who have exhausted all other clinical options. The capacity to expand T cells from healthy immune individuals is providing a new approach to anti-viral immunotherapy, offering rapid off-the-shelf treatment with tailor-made human leukocyte antigen (HLA)-matched T cells. While most of this research has focused on the treatment of latent viral infections, emerging evidence that SARS-CoV-2-specific T cells play an important role in protection against COVID-19 suggests that the transfer of HLA-matched allogeneic off-the-shelf virus-specific T cells could provide a treatment option for patients with active COVID-19 or at risk of developing COVID-19. We initially screened 60 convalescent individuals and based on HLA typing and T-cell response profile, 12 individuals were selected for the development of a SARS-CoV-2-specific T-cell bank. We demonstrate that these T cells are specific for up to four SARS-CoV-2 antigens presented by a broad range of both HLA class I and class II alleles. These T cells show consistent functional and phenotypic properties, display cytotoxic potential against HLA-matched targets and can recognize HLA-matched cells infected with different SARS-CoV-2 variants. These observations demonstrate a robust approach for the production of SARS-CoV-2-specific T cells and provide the impetus for the development of a T-cell repository for clinical assessment.