Background: This study aimed to evaluate short- and long-term humoral and T-cell-specific immune responses to SARS-CoV-2 vaccines in patients with multiple sclerosis (MS) treated with different disease-modifying therapies (DMTs). Methods: Single-center observational longitudinal study including 102 patients with MS who consecutively received vaccination against SARS-CoV-2. Serum samples were collected at baseline and after receiving the second dose of the vaccine. Specific Th1 responses following in vitro stimulation with spike and nucleocapsid peptides were analyzed by quantifying levels of IFN-γ. Serum IgG-type antibodies against the spike region of SARS-CoV-2 were studied by chemiluminescent microparticle immunoassay. Results: Patients undergoing fingolimod and anti-CD20 therapies had a markedly lower humoral response than those treated with other DMTs and untreated patients. Robust antigen-specific T-cell responses were detected in all patients except those treated with fingolimod, who had lower IFN-γ levels than those treated with other DMTs (25.8 pg/mL vs. 868.7 pg/mL, p = 0.011). At mid-term follow-up, a decrease in vaccine-induced anti-SARS-CoV-2 IgG antibodies was observed in all subgroups of patients receiving DMTs, although most patients receiving induction DMTs or natalizumab and non-treated patients remained protected. Cellular immunity was maintained above protective levels in all DMT subgroups except the fingolimod subgroup. Conclusions: SARS-CoV-2 vaccines induce robust and long-lasting humoral and cell-mediated specific immune responses in most patients with MS.