The emergence of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Omicron (B.1.1.529) variant of concern (VOC) has destabilized global efforts to control the impact of coronavirus disease 2019 (COVID-19). Recent data have suggested that B.1.1.529 can readily infect people with naturally acquired or vaccine-induced immunity, facilitated in some cases by viral escape from antibodies that neutralize ancestral SARS-CoV-2. However, severe disease appears to be relatively uncommon in such individuals, highlighting a potential role for other components of the adaptive immune system. We report here that SARS-CoV-2 spike-specific CD4 and CD8 T cells induced by prior infection or BNT162b2 vaccination provide extensive immune coverage against B.1.1.529. The median relative frequencies of SARS-CoV-2 spike-specific CD4 T cells that cross-recognized B.1.1.529 in previously infected or BNT162b2-vaccinated individuals were 84% and 91%, respectively, and the corresponding median relative frequencies for SARS-CoV-2 spike-specific CD8 T cells were 70% and 92%, respectively. Pairwise comparisons across groups further revealed that SARS-CoV-2 spike-reactive CD4 and CD8 T cells were functionally and phenotypically similar in response to the ancestral strain or B.1.1.529. Collectively, our data indicate that established SARS-CoV-2 spike-specific CD4 and CD8 T cell responses, especially after BNT162b2 vaccination, remain largely intact against B.1.1.529.