The risk of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection, hospitalization and death, and the effects of SARS-CoV-2 vaccines in solid organ transplant recipients (SOTRs) is still debated. We performed a nationwide, population-based, matched cohort study, including all Danish SOTRs (n = 5184) and a matched cohort from the general population (n = 41 472). Cox regression analyses were used to calculate incidence rate ratios (IRRs). SOTRs had a slightly increased risk of SARS-CoV-2 infection and were vaccinated earlier than the general population. The overall risk of hospital contact with COVID-19, severe COVID-19, need for assisted respiration, and hospitalization followed by death was substantially higher in SOTRs (IRR: 32.8 95%CI [29.0–37.0], 9.2 [6.7–12.7], 12.5 [7.6–20.8], 12.4 [7.9–12.7]). The risk of hospitalization and death after SARS-CoV-2 infection decreased substantially in SOTRs after the emergence of the Omicron variant (IRR: 0.45 [0.37–0.56], 0.17 [0.09–0.30]). Three vaccinations reduced the risk of SARS-CoV-2 infection only marginally compared to two vaccinations, but SOTRs with three vaccinations had a lower risk of death (IRR: 022 [0.16–0.35]). We conclude that SOTRs have a risk of SARS-CoV-2 infection comparable to the general population, but substantially increased the risk of hospitalization and death following SARS-CoV-2 infection. A third vaccination only reduces the risk of SARS-CoV2 infection marginally, but SOTRs vaccinated 3 times have reduced mortality.