In response to the need for a safe, efficacious vaccine that provides broad immune protection against SARS-CoV-2 infection, we have developed a dual-antigen COVID-19 vaccine. The vaccine delivers both the viral spike (S) protein modified to increase cell-surface expression (S-Fusion) and the viral nucleocapsid (N) protein with an Enhanced T-cell Stimulation Domain (N-ETSD) to enhance MHC class I and II presentation and T-cell responses. The vaccine antigens are delivered using a human adenovirus serotype 5 (hAd5) platform with E1, E2b, and E3 regions deleted that has been shown in previous cancer vaccine studies to be effective in the presence of pre-existing hAd5 immunity. Here, we demonstrate the hAd5 S-Fusion + N-ETSD (hAd5 S + N) vaccine antigens when expressed by dendritic cells (DCs) of previously SARS-CoV-2-infected patients elicit Th1 dominant activation of autologous patient T cells, indicating the vaccine antigens have the potential for generating immune responses in patients previously infected or vaccinated. We further demonstrate that participants in our open-label Phase 1b study of the dual-antigen hAd5 S + N vaccine generate Th1 dominant S- and N-specific T cells after a single prime subcutaneous injection and that the magnitude of these responses were comparable to those seen for T cells from previously infected patients. We further present our in silico prediction of T-cell epitope HLA binding for both the first-wave SARS-CoV-2 ‘A’ strain and the K417N, E484K, and N501Y S as well as the T201I N variants that suggests T-cell responses to the hAd5 S + N vaccine will retain efficacy against these variants. These findings that the dual-antigen hAd5 S + N vaccine elicits SARS-CoV-2-relevant T-cell responses and that such cell-mediated protection is likely to be sustained against emerging variants supports the testing of this vaccine as a universal booster that would enhance and broaden existing immune protection conferred by currently approved S-based vaccines.