BNT162b2, a lipid nanoparticle (LNP) formulated nucleoside-modified messenger RNA (mRNA) encoding the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spike protein (S) stabilized in the prefusion conformation, has demonstrated 95% efficacy to prevent coronavirus disease 2019 (COVID-19). Recently, we reported preliminary BNT162b2 safety and antibody response data from an ongoing placebo-controlled, observer-blinded phase 1/2 vaccine trial1. We present here antibody and T cell responses from a second, non-randomized open-label phase 1/2 trial in healthy adults, 19-55 years of age, after BNT162b2 prime/boost vaccination at 1 to 30 µg dose levels. BNT162b2 elicited strong antibody responses, with S-binding IgG concentrations above those in a COVID-19 human convalescent sample (HCS) panel. Day 29 (7 days post-boost) SARS-CoV-2 serum 50% neutralising geometric mean titers were 0.3-fold (1 µg) to 3.3-fold (30 µg) those of the HCS panel. The BNT162b2-elicited sera neutralised pseudoviruses with diverse SARS-CoV-2 S variants. Concurrently, in most participants, S-specific CD8+ and T helper type 1 (TH1) CD4+ T cells had expanded, with a high fraction producing interferon-γ (IFNγ). Using peptide MHC multimers, the epitopes recognised by several BNT162b2-induced CD8+ T cells when presented on frequent MHC alleles were identified. CD8+ T cells were shown to be of the early-differentiated effector-memory phenotype, with single specificities reaching 0.01-3% of circulating CD8+ T cells. In summary, vaccination with BNT162b2 at well tolerated doses elicits a combined adaptive humoral and cellular immune response, which together may contribute to protection against COVID-19.