The SARS-CoV-2 Omicron variant (B.1.1.529) has multiple spike protein mutations that contribute to viral escape from antibody neutralization and reduce vaccine protection from infection. The extent to which other components of the adaptive response such as T cells may still target Omicron and contribute to protection from severe outcomes is unknown. Here we assessed the ability of T cells to react to Omicron spike protein in participants who were vaccinated with Ad26.CoV2.S or BNT162b2, or unvaccinated convalescent COVID-19 patients (n = 70). Between 70% and 80% of the CD4 and CD8 T cell response to spike was maintained across study groups. Moreover, the magnitude of Omicron cross-reactive T cells was similar for Beta (B.1.351) and Delta (B.1.617.2) variants, despite Omicron harbouring considerably more mutations. In patients who were hospitalized with Omicron infections (n = 19), there were comparable T cell responses to ancestral spike, nucleocapsid and membrane proteins to those in patients hospitalized in previous waves dominated by the ancestral, Beta or Delta variants (n = 49). Thus, despite extensive mutations and reduced susceptibility to neutralizing antibodies of Omicron, the majority of T cell responses induced by vaccination or infection cross-recognize the variant. It remains to be determined whether well-preserved T cell immunity to Omicron contributes to protection from severe COVID-19 and is linked to early clinical observations from South Africa and elsewhere.