The severe acute respiratory distress syndrome coronavirus-2 (SARS-CoV-2) Omicron variant (B.1.1.529) is spreading rapidly, even in vaccinated individuals, raising concerns about immune escape. Here, we studied neutralizing antibodies and T-cell responses targeting SARS-CoV-2 D614G (wildtype, WT), and the B.1.351 (Beta), B.1.617.2 (Delta), and B.1.1.529 (Omicron) variants of concern (VOC) in a cohort of 60 health care workers after immunization with ChAdOx-1 S, Ad26.COV2.S, mRNA-1273 or BNT162b2. High binding antibody levels against WT SARS-CoV-2 spike (S) were detected 28 days after vaccination with both mRNA vaccines (mRNA-1273 or BNT162b2), which significantly decreased after 6 months. In contrast, antibody levels were lower after Ad26.COV2.S vaccination but did not wane. Neutralization assays with infectious virus showed consistent cross-neutralization of the Beta and Delta variants, but neutralization of Omicron was significantly lower or absent (up to a 34-fold decrease compared to WT). Notably, BNT162b2 booster vaccination after either two mRNA-1273 immunizations or Ad26.COV.2 priming partially restored neutralization of the Omicron variant, but responses were still up to-17-fold decreased compared to WT. SARS-CoV-2-specific T-cells were detected up to 6 months after all vaccination regimens, with more consistent detection of specific CD4+ than CD8+ T-cells. No significant differences were detected between WT- and variant-specific CD4+ or CD8+ T-cell responses, including Omicron, indicating minimal escape at the T-cell level. This study shows that vaccinated individuals retain T-cell immunity to the SARS-CoV-2 Omicron variant, potentially balancing the lack of neutralizing antibodies in preventing or limiting severe COVID-19. Booster vaccinations are needed to further restore Omicron cross-neutralization by antibodies.