The vaccination campaign for the Veneto region (northeastern Italy) started on 27 December 2020. As of early December 2021, 75.1% of the whole Veneto population has been fully vaccinated. Vaccine efficacy has been demonstrated in many clinical trials, but reports on real-world contexts are still necessary. We conducted a retrospective cohort study on 2,233,399 residents in the Veneto region to assess the reduction in the COVID-19 burden, taking different outcomes into consideration. First, we adopted a non-brand-specific approach borrowed from survival analysis to estimate the effectiveness of vaccination against SARS-CoV-2 in preventing infections, hospitalizations, and deaths. We used t-tests and multivariate regressions to examine vaccine impact on breakthrough infections, in terms of the persistence of positivity and the length of hospital stays. Evidence emerging from this study suggests that unvaccinated individuals are significantly more likely to become infected, need hospitalization, and are at a higher risk of death from COVID-19 than those given at least one dose of vaccine. Cox models indicate that the effectiveness of full vaccination is 88% against infection, 94% against hospitalization, and 95% against death. Multivariate regressions suggest that vaccination is significantly correlated with a shorter period of positivity and shorter hospital stays, with each step toward completion of the vaccination cycle coinciding with a reduction of 3.3 days in the persistence of positivity and 2.3 days in the length of hospital stay.