Background/Objectives: The aim of our study was to investigate B cell and T cell responses in people with multiple sclerosis (PwMS) treated with ocrelizumab, a humanized anti-CD20 antibody, who were vaccinated with second and/or booster doses of various vaccine brands against COVID-19. Additionally, we detected the outcomes related to COVID-19 in PwMS after vaccination, based on follow-up for at least 12 months. Methods: We enrolled 91 PwMS on ocrelizumab and 42 healthy controls (HCs) in a prospective, single-center study, conducted at the Clinic of Neurology, UCCS, between January 2022 and October 2024. The serological responses were measured using the spike receptor-binding domain (RBD) Architect SARS-CoV-2 IgG Quant kit (Abbot), and cellular responses were measured by quantifying IFN-γ secretion in blood incubated with SARS-CoV-2 antigens. Results: A total of 58.2% (53/91) of PwMS on ocrelizumab and 100% of the HCs (42/42) were seropositive after a second or booster vaccination (p < 0.001), irrespective of the vaccine brand received. Anti-spike antibody levels were significantly lower in PwMS on ocrelizumab compared to the HCs (p < 0.001), again irrespective of the vaccine type. Interferon-γ responses were detected in 95.6% of the PwMS receiving ocrelizumab therapy and 97.6% of HCs after vaccination (p = 0.570). In our cohort, PCR-confirmed SARS-CoV-2 infections after vaccination occurred in a similar proportion of the PwMS (45/91, 49.5%) and HCs (15/32, 46.9%) (p = 0.139). Most of the PwMS (36/45, 79.2%) and HCs (13/15, 87.8%) had COVID-19 of mild severity. Conclusions: PwMS treated with ocrelizumab developed diminished humoral and robust cellular responses following two and three SARS-CoV-2 vaccinations. The obtained immunity after SARS-CoV-2 vaccination may translate into lower incidence and severity of COVID-19.