Objective: To examine the association between paternal antidepressant use at conception and offspring preterm birth, malformations, autism spectrum disorder, and intellectual disability. Design: Observational prospective cohort study with regression methods, and negative control comparison. Setting: Sweden nationwide. Participants: 170 508 children conceived from 29 July 2005 and born in 2006-07, followed up to 2014 at age 8-9 years. This cohort included 3983 children born to fathers receiving antidepressant treatment during the conception period (that is, from four weeks before conception to four weeks after), a control group of 164 492 children not exposed to paternal antidepressant use, and a negative control comparison group of 2033 children born to fathers who did not use antidepressants during the conception period but began antidepressant treatment later during the pregnancy period (that is, from four weeks after conception to childbirth). Main outcome measure: Offspring preterm birth, malformation diagnosed at birth, diagnosis of autism spectrum disorder, and diagnosis of intellectual disability. Results: Paternal antidepressant use during conception was not associated with preterm birth (adjusted odds ratio 0.91 (95% confidence interval 0.79 to 1.04)) or malformations (1.06 (0.90 to 1.26)) using logistic regression, compared with offspring born to unexposed fathers. No association was seen between antidepressant use during conception and autism (adjusted hazard ratio 1.13 (0.84 to 1.53)) or intellectual disability (0.82 (0.51 to 1.31)) using Cox regression. In children whose fathers initiated antidepressant treatment during pregnancy, results were similar for all outcomes apart from intellectual disability, which had an increased adjusted hazard ratio (1.66 (1.06 to 2.59)). Compared with the 2033 children whose fathers initiated antidepressant treatment during pregnancy, the 3983 children exposed to paternal use of antidepressants at conception had no differences in preterm birth, malformation, and autism, but a reduced risk of intellectual disability (adjusted hazard ratio 0.49 (0.26 to 0.93)). Conclusion: Paternal intake of antidepressants during the period around conception is safe with respect to the risk of the four major adverse outcomes in offspring - preterm birth, malformation, autism, or intellectual disability.