Background: The post-acute sequelae of SARS-CoV-2 (PASC) infection have caused a significant impact on our health system, but there is limited evidence of approved drugs focused on its prevention. Our objective was to identify risk factors that can determine the presence of PASC, with special attention to the treatment received in the acute phase, and to describe the profile of persistent symptoms in a multidisciplinary Post-Coronavirus Disease-19 (COVID-19) Unit. Methods: This one-year prospective observational study included patients following an acute COVID-19 infection, irrespective of whether they required hospital admission. A standardized symptom questionnaire and blood sampling were performed at the first follow-up visit, and demographic and clinical electronic data were collected. We compared subjects with PASC with those who had fully recovered. Multivariate logistic regression was performed to identify factors associated with PASC in hospitalized patients, and Kaplan–Meier curves were used to assess duration of symptoms according to disease severity and treatments received in the acute phase. Results: 1966 patients were evaluated; 1081 had mild disease, 542 moderate and 343 severe; around one third of the subjects had PASC, and were more frequently female, with obesity, asthma, and eosinophilia during acute COVID-19 disease. Patients who received treatment with dexamethasone and remdesivir during the course of the acute illness showed a lower median duration of symptoms, compared with those who received none of these treatments. Conclusion: Treatment with dexamethasone and/or remdesivir may be useful to reduce the impact of PASC secondary to SARS-CoV-2 infection. In addition, we identified female gender, obesity, asthma, and disease severity as risk factors for having PASC.