Being unable to suppress SARS-CoV-2 transmission, the majority of countries worldwide have resorted to a mitigation approach towards COVID-19, allowing some degree of viral circulation in the population. Here, we investigate the expected outcomes of the interplay between vaccination rollout and adaptive mitigation measures constantly altering the epidemic trajectory and keeping the reproduction number around the unit. Using a novel mathematical modeling framework, we estimate that, for vaccination capacities of at least 4 daily doses administered per 1,000 inhabitants, a complete release of mitigation measures can be expected within 7 to 13 months since the start of vaccination, with a two-year cumulative incidence of deaths between 0.18 and 0.46 per 1,000 population. A heavier burden of deaths and a delayed <<return-to-normal>> is expected for lower vaccine capacities, if viral transmissibility exceeds by >60% the one estimated at the beginning of the pandemic, or if vaccine protection is short-lived. Failure to prioritize the elderly or a premature release of mitigation measures after vaccination of the most fragile will conspicuously increase the expected mortality. Finally, strategies oriented to prioritize the suppression of SARS-CoV-2 by maintaining strict restrictions will take a similar time as a mitigation approach, possibly resulting in acceptability issues. Persisting unknowns about the evolving epidemiology of SARS-CoV-2 variants and on the effectiveness of available and upcoming vaccines may warrant a future reassessment of these conclusions.