Class I- and Class II-restricted epitopes have been identified across the SARS-CoV-2 structural proteome. Vaccine-induced and post-infection SARS-CoV-2 T-cell responses are associated with COVID-19 recovery and protection, but the precise role of T-cell responses remains unclear, and how post-infection vaccination ('hybrid immunity') further augments this immunity To accomplish these goals, we studied healthy adult healthcare workers who were (a) uninfected and unvaccinated (n = 12), (b) uninfected and vaccinated with Pfizer-BioNTech BNT162b2 vaccine (2 doses n = 177, one dose n = 1) or Moderna mRNA-1273 vaccine (one dose, n = 1), and (c) previously infected with SARS-CoV-2 and vaccinated (BNT162b2, two doses, n = 6, one dose n = 1; mRNA-1273 two doses, n = 1). Infection status was determined by repeated PCR testing of participants. We used FluoroSpot Interferon-gamma (IFN-γ) and Interleukin-2 (IL-2) assays, using subpools of 15-mer peptides covering the S (10 subpools), N (4 subpools) and M (2 subpools) proteins. Responses were expressed as frequencies (percent positive responders) and magnitudes (spot forming cells/106 cytokine-producing peripheral blood mononuclear cells [PBMCs]). Almost all vaccinated participants with no prior infection exhibited IFN-γ, IL-2 and IFN-γ+IL2 responses to S glycoprotein subpools (89%, 93% and 27%, respectively) mainly directed to the S2 subunit and were more robust than responses to the N or M subpools. However, in previously infected and vaccinated participants IFN-γ, IL-2 and IFN-γ+IL2 responses to S subpools (100%, 100%, 88%) were substantially higher than vaccinated participants with no prior infection and were broader and directed against nine of the 10 S glycoprotein subpools spanning the S1 and S2 subunits, and all the N and M subpools. 50% of uninfected and unvaccinated individuals had IFN-γ but not IL2 or IFN-γ+IL2 responses against one S and one M subpools that were not increased after vaccination of uninfected or SARS-CoV-2-infected participants. Summed IFN-γ, IL-2, and IFN-γ+IL2 responses to S correlated with IgG responses to the S glycoprotein. These studies demonstrated that vaccinations with BNT162b2 or mRNA-1273 results in T cell-specific responses primarily against epitopes in the S2 subunit of the S glycoprotein, and that individuals that are vaccinated after SARS-CoV-2 infection develop broader and greater T cell responses to S1 and S2 subunits as well as the N and M proteins.