During the ongoing coronavirus disease COVID-19 pandemic, many individuals were infected with and have cleared the virus, developing virus-specific antibodies and effector/memory T cells. An important unanswered question is what levels of T cell and antibody responses are sufficient to protect from the infection. In 5340 Moscow residents, we evaluated anti-SARS-CoV-2 IgM/IgG titers and frequencies of the T cells specific to the membrane, nucleocapsid, and spike proteins of SARS-CoV-2, using IFNγ ELISpot assay. Additionally, we evaluated the fractions of virus-specific CD4+ and CD8+ T cells using intracellular staining of IFNγ and IL2 followed by flow cytometry. We analyzed the COVID-19 rates as a function of the assessed antibody and T cell responses, using the Kaplan-Meyer estimator method, for up to 300 days post-inclusion. We showed that T cell and antibody responses are closely interconnected and are commonly induced concurrently. Magnitudes of both responses inversely correlated with infection probability. Individuals positive for both responses demonstrated the highest levels of protectivity against the SARS-CoV-2 infection. A comparable level of protection was found in individuals with antibody response only, while the T cell response by itself granted only intermediate protection. We found that the contribution of the virus-specific antibodies to protection against the SARS-CoV-2 infection is more pronounced than that of the T cells. The data on the virus-specific IgG titers may be instructive for making decisions in personalized health care and public anti-COVID-19 policies.