(1) Background: SARS-CoV-2 infections are associated with an increased risk of hospital admissions especially in the elderly (age ≥ 65 years) and people with multiple comorbid conditions. (2) Methods: We investigated the effect of additional booster vaccinations following the primary vaccination series of mRNA, inactivated whole virus, or vector vaccines on infections with the SARS-CoV-2 delta variant in the total Hungarian elderly population. The infection, hospital admission, and 28-day all-cause mortality of elderly population was assessed. (3) Results: A total of 1,984,176 people fulfilled the criteria of elderly including 299,216 unvaccinated individuals, while 1,037,069 had completed primary vaccination and 587,150 had obtained an additional booster. The primary vaccination series reduced the risk of infection by 48.88%, the risk of hospital admission by 71.55%, and mortality by 79.87%. The booster vaccination had an additional benefit, as the risk of infection, hospital admission, and all-cause mortality were even lower (82.95%; 92.71%; and 94.24%, respectively). Vaccinated patients needing hospitalization suffered significantly more comorbid conditions, indicating a more vulnerable population. (4) Conclusions: Our data confirmed that the primary vaccination series and especially the booster vaccination significantly reduced the risk of the SARS-CoV-2 delta-variant-associated hospital admission and 28-day all-cause mortality in the elderly despite significantly more severe comorbid conditions.