T cells are a critical component of the response to SARS-CoV-2, but their kinetics after infection and vaccination are insufficiently understood. Using "spheromer" peptide-MHC multimer reagents, we analyzed healthy subjects receiving two doses of the Pfizer/BioNTech BNT162b2 vaccine. Vaccination resulted in robust spike-specific T cell responses for the dominant CD4⁺ (HLA-DRB1^∗15:01/S191) and CD8⁺ (HLA-A^∗02/S691) T cell epitopes. Antigen-specific CD4⁺ and CD8⁺ T cell responses were asynchronous, with the peak CD4⁺ T cell responses occurring 1 week post the second vaccination (boost), whereas CD8⁺ T cells peaked 2 weeks later. These peripheral T cell responses were elevated compared with COVID-19 patients. We also found that previous SARS-CoV-2 infection resulted in decreased CD8⁺ T cell activation and expansion, suggesting that previous infection can influence the T cell response to vaccination.