Since early 2022, various Omicron variants have dominated the SARS-CoV-2 pandemic in most countries. All Omicron variants are B-cell immune escape variants, and antibodies induced by first-generation COVID-19 vaccines or by infection with earlier SARS-CoV-2 variants largely fail to protect individuals from Omicron infection. In the present study, we investigated the effect of Omicron infections in triple-vaccinated and in antigen-naive individuals. We show that Omicron breakthrough infections occurring 2–3.5 months after the third vaccination restore B-cell and T-cell immune responses to levels similar to or higher than those measured 14 days after the third vaccination, including the induction of Omicron-neutralizing antibodies. Antibody responses in breakthrough infection derived mostly from cross-reacting B cells, initially induced by vaccination, whereas Omicron infections in antigen-naive individuals primarily generated B cells binding to the Omicron but not the Wuhan spike protein. Although antigen-naive individuals mounted considerable T-cell responses after infection, B-cell responses were low, and neutralizing antibodies were frequently below the limit of detection. In summary, the detection of Omicron-associated B-cell responses in primed and in antigen-naive individuals supports the application of Omicron-adapted COVID-19 vaccines, but calls into question their suitability if they also contain/encode antigens of the original Wuhan virus.