In Italy, at the end of 2020, a voluntary immunization plan against COVID-19 was introduced, involving elderly among the first target categories. The aim of this study was to assess, through an online questionnaire, the acceptance of COVID-19 vaccination in a sample of older adults from southern Italy. Of a total of 1041 respondents (41.7% males, mean age 76.6 ± 6.5), 965 (92.7%) were vaccinated or willing to be vaccinated against COVID-19, although less than half of the sample was favorable to vaccinations and agreed with mandatory immunization. Acceptance of COVID-19 vaccination was found to be positively related with higher educational level (OR = 1.875, CI95% = 1.113–3.161; p = 0.018) and having social/mass media as a main source of information (OR = 2.415 CI95% = 1.358–4.296, p = 0.003). On the contrary, an inverse relationship was found between acceptance of COVID-19 vaccination and having fulfilled the questionnaire after the introduction of green pass (OR = 0.218, CI95% = 0.129–0.369; p < 0.001). Therefore, although this evidence needs to be further confirmed, it is possible to agree with previous studies reporting that compulsory measures, such as green pass implementation, must be accompanied by effective education and information strategies of the target population.