The SARS-CoV-2 Omicron variant has multiple Spike (S) protein mutations that contribute to escape from the neutralizing antibody responses, and reducing 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. We assessed the ability of T cells to react with Omicron spike in participants who were vaccinated with Ad26.CoV2.S or BNT162b2, and in unvaccinated convalescent COVID-19 patients (n = 70). We found that 70-80% 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 to that of the Beta and Delta variants, despite Omicron harbouring considerably more mutations. Additionally, in Omicron-infected hospitalized patients (n = 19), there were comparable T cell responses to ancestral spike, nucleocapsid and membrane proteins to those found in patients hospitalized in previous waves dominated by the ancestral, Beta or Delta variants (n = 49). These results demonstrate that despite Omicron's extensive mutations and reduced susceptibility to neutralizing antibodies, the majority of T cell response, induced by vaccination or natural infection, cross-recognises the variant. Well-preserved T cell immunity to Omicron is likely to contribute to protection from severe COVID-19, supporting early clinical observations from South Africa.