Background: Preoperative COVID-19 has been associated with excess postoperative morbi-mortality. Consequently, guidelines were developed that recommended the postponement of surgery for at least 7 weeks after the infection. We hypothesised that vaccination against the SARS-CoV-2 and the large predominance of the Omicron variant attenuated the effect of a preoperative COVID-19 on the occurrence of postoperative respiratory morbidity. Methods: We conducted a prospective cohort study in 41 French centres between 15 March and 30 May 2022 (ClinicalTrials NCT05336110), aimed at comparing the postoperative respiratory morbidity between patients with and without preoperative COVID-19 within 8 weeks prior to surgery. The primary outcome was a composite outcome combining the occurrence of pneumonia, acute respiratory failure, unexpected mechanical ventilation, and pulmonary embolism within the first 30 postoperative days. Secondary outcomes were 30-day mortality, hospital length-of-stay, readmissions, and non-respiratory infections. The sample size was determined to have 90% power to identify a doubling of the primary outcome rate. Adjusted analyses were performed using propensity score modelling and inverse probability weighting. Findings: Of the 4928 patients assessed for the primary outcome, of whom 92.4% were vaccinated against the SARS-CoV-2, 705 had preoperative COVID-19. The primary outcome was reported in 140 (2.8%) patients. An 8-week preoperative COVID-19 was not associated with increased postoperative respiratory morbidity (odds ratio 1.08 [95% CI 0.48-2.13]; p = 0.83). None of the secondary outcomes differed between the two groups. Sensitivity analyses concerning the timing between COVID-19 and surgery, and the clinical presentations of preoperative COVID-19 did not show any association with the primary outcome, except for COVID-19 patients with ongoing symptoms the day of surgery (OR 4.29 [1.02-15.8]; p = 0.04). Interpretation: In our Omicron-predominant, highly immunised population undergoing general surgery, a preoperative COVID-19 was not associated with increased postoperative respiratory morbidity.