Breakthrough infections with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants have been reported frequently in vaccinated individuals with waning immunity. In particular, a cluster of over 1000 infections with the SARS-CoV-2 delta variant was identified in a predominantly fully vaccinated population in Provincetown, Massachusetts in July 2021. In this study, vaccinated individuals who tested positive for SARS-CoV-2 (n = 16) demonstrated substantially higher serum antibody responses than vaccinated individuals who tested negative for SARS-CoV-2 (n = 23), including 32-fold higher binding antibody titers and 31-fold higher neutralizing antibody titers against the SARS-CoV-2 delta variant. Vaccinated individuals who tested positive also showed higher mucosal antibody responses in nasal secretions and higher spike protein-specific CD8+ T cell responses in peripheral blood than did vaccinated individuals who tested negative. These data demonstrate that fully vaccinated individuals developed robust anamnestic antibody and T cell responses after infection with the SARS-CoV-2 delta variant. Moreover, these findings suggest that population immunity will likely increase over time by a combination of widespread vaccination and breakthrough infections.