SARS-CoV-2 has caused morbidity and mortality across the globe. As the virus spreads, new variants are arising that show enhanced capacity to bypass preexisting immunity. To understand the memory response to SARS-CoV-2, here, we monitored SARS-CoV-2–specific T and B cells in a longitudinal study of infected and recovered golden hamsters (Mesocricetus auratus). We demonstrated that engagement of the innate immune system after SARS-CoV-2 infection was delayed but was followed by a pronounced adaptive response. Moreover, T cell adoptive transfer conferred a reduction in virus levels and rapid induction of SARS-CoV-2–specific B cells, demonstrating that both lymphocyte populations contributed to the overall response. Reinfection of recovered animals with a SARS-CoV-2 variant of concern showed that SARS-CoV-2–specific T and B cells could effectively control the infection that associated with the rapid induction of neutralizing antibodies but failed to block transmission to both naïve and seroconverted animals. These data suggest that the adaptive immune response to SARS-CoV-2 is sufficient to provide protection to the host, independent of the emergence of variants.