Increased COVID-19-related morbidity and mortality have been reported in solid organ transplant recipients (SOTRs). Most studies are underpowered for rigorous matching. We report infections, hospitalization, ICU care, mortality from COVID-19, and pertinent vaccination data in Swedish SOTRs 2020–2021. We conducted a nationwide cohort study, encompassing all Swedish residents. SOTRs were identified with ICD-10 codes and immunosuppressant prescriptions. Comparison cohorts were weighted based on a propensity score built from potential confounders (age, sex, comorbidities, socioeconomic factors, and geography), which achieved a good balance between SOTRs and non-SOTR groups. We included 10,372,033 individuals, including 9073 SOTRs. Of the SARS-CoV-2 infected, 47.3% of SOTRs and 19% of weighted comparator individuals were hospitalized. ICU care was given to 8% of infected SOTRs and 2% of weighted comparators. The case fatality rate was 7.7% in SOTRs, 6.2% in the weighted comparison cohort, and 1.3% in the unweighted comparison cohort. SOTRs had an increased risk of contracting COVID-19 (HR = 1.15 p < 0.001), being hospitalized (HR = 2.89 p < 0.001), receiving ICU care (HR = 4.59 p < 0.001), and dying (HR = 1.42 p < 0.001). SOTRs had much higher morbidity and mortality than the general population during 2020–2021. Also compared with weighted comparators, SOTRs had an increased risk of contracting COVID-19, being hospitalized, receiving ICU care, and dying. In Sweden, SOTRs were vaccinated earlier than weighted comparators. Lung transplant recipients had the worst outcomes. Excess mortality among SOTRs was concentrated in the second half of 2021.