AZD1222 (ChAdOx1 nCoV-19), a replication-deficient simian adenovirus-vectored vaccine, has demonstrated safety, efficacy, and immunogenicity against coronavirus disease 2019 (COVID-19) in clinical trials and real-world studies. We characterized CD4+ and CD8+ T-cell responses induced by AZD1222 vaccination in peripheral blood mononuclear cells (PBMCs) from 280 unique vaccine recipients aged 18-85 years who enrolled in the phase 2/3 COV002 trial. Total spike-specific CD4+ T cell helper type 1 (Th1) and CD8+ T-cell responses were significantly increased in AZD1222-vaccinated adults of all ages following two doses of AZD1222. CD4+ Th2 responses following AZD1222 vaccination were not detected. Furthermore, AZD1222-specific Th1 and CD8+ T cells both displayed a high degree of polyfunctionality in all adult age groups. T-cell receptor (TCR) β sequences from vaccinated participants mapped against TCR sequences known to react to SARS-CoV-2 revealed substantial breadth and depth across the SARS-CoV-2 spike protein for the AZD1222-induced CD4+ and CD8+ T-cell responses. Overall, AZD1222 vaccination induced a robust, polyfunctional Th1-dominated T-cell response, with broad CD4+ and CD8+ T-cell coverage across the SARS-CoV-2 spike protein. One Sentence Summary: Polyfunctional CD4+ and CD8+ T-cell responses are elicited against the SARS-CoV-2 spike protein following vaccination with AZD1222.