This is a multicenter, double- blind extension study of Oral Budesonide Suspension (OBS) in adults and adolescents (11 to 55 years of age, inclusive) with Eosinophilic Esophagitis (EoE) who have completed participation in the SHP621-301 induction study (NCT02605837). The primary objective is to evaluate the maintenance of efficacy of OBS over 36 weeks. Maintenance of efficacy will be measured by the peak eosinophilic count and Dysphagia Symptom Questionnaire (DSQ) score.