There is an urgent need to understand the nature of immune responses against SARS-CoV-2, to inform risk-mitigation strategies for people living with HIV (PLWH). We show that the majority of PLWH, controlled on ART, mount a functional adaptive immune response to SARS-CoV-2. Humoral and SARS-CoV-2-specific T cell responses are comparable between HIV-positive and negative subjects and persist 5-7 months following predominately mild COVID-19 disease. T cell responses against Spike, Membrane and Nucleocapsid are the most prominent, with SARS-CoV-2-specific CD4 T cells outnumbering CD8 T cells. We further show that the overall magnitude of SARS-CoV-2-specific T cell responses relates to the size of the naive CD4 T cell pool and the CD4:CD8 ratio in PLWH, in whom disparate antibody and T cell responses are observed. These findings suggest that inadequate immune reconstitution on ART, could hinder immune responses to SARS-CoV-2 with implications for the individual management and vaccine effectiveness in PLWH.