Perioperative exposure to opioids is associated with adverse outcomes. We aim to determine the associations between surgery and subsequent opioid overdose, an acute event, and a new diagnosis of opioid use disorder (OUD), a chronic relapsing disease, in parallel. This retrospective cohort study of US veterans used surgery as exposure and the two outcomes were (1) occurrence of overdose and (2) new diagnosis of OUD in the first postoperative year. Surgical group was matched to the reference controls based on the propensity score of having surgery, and matched logistic regression was used to calculate the odds ratio (OR). A total of 261 208 surgical patients were matched to 479 531 controls. Overdose occurred in 1893 (0.7%) of the surgical patients and in 518 (0.1%) of the matched controls in the first postoperative year (OR, 6.71; 95% confidence interval [CI], 5.80-7.75; P < .001). Among patients with no history of OUD, surgery was also associated with a new diagnosis of OUD in the first postoperative year (OR, 1.13; 95% CI, 1.02-1.24; P = .015). The postoperative period is strongly associated with opioid overdose, but only weakly associated with new diagnosis of OUD. This is likely due to the difficulty of diagnosing OUD in the postoperative period. This is the first study that has examined opioid overdose and new-onset OUD in the postoperative period in parallel. Our analysis suggests different risk factors for each, as well as different strengths of association with surgery. More sensitive diagnostic criteria for postoperative OUD are needed to promptly diagnose and treat this condition. (Am J Addict 2020;00:00-00).