Objective: To compare the risk of a positive severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) test and coronavirus disease 2019 (COVID-19) outcomes in people with HIV (PWH) with the general population, and estimate the association with vaccination status. Design: A nationwide, population based, matched cohort studyMethods: We included all Danish PWH ≥18years (n=5276) and an age and sex-matched general population cohort (n=42 308). We used Cox regression analyses to calculate (adjusted) incidence rate ratios [(a)IRR] and further stratified and restricted the analyses. Results: We observed no major difference in risk of first positive SARS-CoV-2 test [aIRR: 0.8 (95% confidence interval (CI): 0.8-0.9)], but a higher risk of first hospital contact with COVID-19 and hospitalization with severe COVID-19 for PWH vs. controls [IRR: 2.0; (1.6-2.5), 1.8 (1.4-2.3)]. Risk of first hospitalization decreased substantially in PWH with calendar time [first half of year 2022 vs. 2020 IRR: 0.3; (0.2-0.6)], whereas the risk compared to population controls remained almost twofold increased. We did not observe increased risk of death after SARS-CoV-2 infection [aIRR: 0.7 (95% CI: 0.3-2.0)]. Compared to PWH who had received two vaccines PWH who receiving a third vaccine had reduced risk of first positive SARS-CoV-2 test, death (individuals ≥60years) and hospitalization [aIRR: 0.9 (0.7-1.0); 0.2 (0.1-0.7); 0.6 (0.2-1.2)]. Conclusion: PWH have almost the same risk of a positive SARS-CoV-2 test as the general population. Although risk of hospital contacts and severe outcomes following SARS-CoV-2 infection is increased, the risk of death does not seem to be substantially increased. Importantly, a third vaccine is associated with reduced risk of infection, and death.