The development and persistence of SARS-CoV-2-specific immune response in immunocompetent (IC) and immunocompromised patients is crucial for long-term protection. Immune response to SARS-CoV-2 infection was analysed in 57 IC and 15 solid organ transplanted (TX) patients. Antibody responses were determined by ELISA and neutralization assay. T-cell response was determined by stimulation with peptide pools of the Spike, Envelope, Membrane, and Nucleocapsid proteins with a 20-h Activation Induced Marker (AIM) and 7-day lymphoproliferative assays. Antibody response was detected at similar levels in IC and TX patients. Anti-Spike IgG, IgA and neutralizing antibodies persisted for at least one year, while anti-Nucleocapsid IgG declined earlier. Patients with pneumonia developed higher antibody levels than patients with mild symptoms. Similarly, both rapid and proliferative T-cell responses were detected within the first two months after infection at comparable levels in IC and TX patients, and were higher in patients with pneumonia. T-cell response persisted for at least one year in both IC and TX patients. Spike, Membrane, and Nucleocapsid proteins elicited the major CD4+ and CD8+ T-cell responses, whereas the T-cell response to Envelope protein was negligible. After SARS-CoV-2 infection, antibody and T-cell responses develop rapidly and persist over time in both immunocompetent and transplanted patients.