Background and purpose: Several smaller, community-based studies have suggested a link between sleep disorders and dementia with a focus on sleep as a modifiable risk factor for dementia. Studies on neurodegenerative diseases are prone to reverse causation, and few studies have examined the association with long follow-up time. Our aim was to explore the possible association between sleep disorders and late-onset dementia in an entire population. Methods: In a nationwide cohort with 40-year follow-up, associations between hospital-based sleep disorder diagnoses and late-onset dementia were assessed. Incidence rate ratios (IRR) were calculated using Poisson regression. Results: The cohort consisted of 1,491,276 people. Those with any sleep disorder had a 17% higher risk of dementia (IRR 1.17, 95% confidence interval [CI] 1.11–1.24) compared to people with no sleep disorder, adjusted for age, sex, calendar year, highest attained educational level at age 50, and somatic and psychiatric comorbidity. The risk of dementia was significantly increased 0–5 years after sleep disorder diagnosis (IRR 1.35, 95% CI 1.25–1.47), whilst the association after 5 years or more was non-significant (1.05, 95% CI 0.97–1.13). Conclusions: Our findings show an increased short-term risk of dementia following a hospital-based sleep disorder diagnosis, whilst weaker evidence of a long-term risk was found. This could potentially point towards sleep disorders as an early symptom of dementia. Further research is needed to distinguish sleep disorders as an early symptom of dementia, a risk factor, or both.