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.