Objectives We determined the incidence and prevalence of Addison’s disease (AD) among persons with or without type 1 diabetes mellitus (T1DM) in nationwide, matched cohort studies. Methods Persons with T1DM were identified from the Swedish National Diabetes Register and each was matched for age, sex, year and county to five controls randomly selected from the general population. Persons with AD were identified from the Swedish National Inpatient Register. Baseline demographics and seasonal onset variation of AD were presented by descriptive statistics. Prevalence and incidence were estimated by proportions and incidence rates, respectively. Times to AD were analyzed using the Cox proportional hazard model. Results Between 1998 and 2013, 66 persons with T1DM were diagnosed with AD at a mean age (s.d.) of 36.4 (13.0) years among 36 514 persons with T1DM, while 32 were diagnosed with AD at a mean age of 42.7 (15.2) years among 182 570 controls. The difference in mean age at diagnosis of AD between the groups was 6.3 years (P value = 0.036). The incidence of AD for a person with or without T1DM was therefore 193 and 18 per million person-years, respectively. The adjusted relative risk increase of developing AD in T1DM was 10.8 (95% CI: 7.1–16.5). The highest incidence of AD was observed during February–March and September–October. The prevalence of AD in persons with or without T1DM in December 2012 was 3410 and 208 per million, respectively. The odds ratio for AD in persons with T1DM vs controls was 16.5 (95% CI: 11.1–24.5). Conclusion The risk to develop AD among persons with T1DM is more than 10 times higher than in persons without T1DM. Persons with T1DM develop AD at a younger age. The incidence of AD may have a seasonal pattern.