A Study of Vedolizumab in Children and Teenagers With Ulcerative Colitis or Crohn's Disease

The drug being tested in this study is vedolizumab. Vedolizumab is being tested to treat pediatric participants with moderate to severe active UC or CD who achieved clinical response following open-label vedolizumab intravenous (IV) therapy. The study will look at the pharmacokinetics, safety, and immunogenicity of vedolizumab. The study will enroll approximately 70 patients. During the Induction Period participants will receive 3 doses of vedolizumab IV infusion at Day 1, Week 2, and Week 6 based on their weight at Baseline as: * Participants ≥30 kilograms (kg), Vedolizumab (High Dose) * Participants \>15 to \<30 kg, Vedolizumab (Medium Dose) * Participants ≥10 to ≤15 kg, Vedolizumab (Low Dose) At Week 14, participants who achieve clinical response will be assigned to one of the following groups, stratified by weight to receive vedolizumab 108 mg SC injection during the 20-week Maintenance Period: * Participants ≥30 kg, Vedolizumab 108 mg once every 2 weeks (Q2W) * Participants ≥10 to \<30 kg, Vedolizumab 108 mg once every 4 weeks (Q4W) This multi-center trial will be conducted globally. After the Week 34 end of treatment (EOT) visit assessments have been completed, participants may be eligible to receive continued treatment with vedolizumab SC in an extension study, whereas participants who do not qualify to receive continued treatment in the extension study or participants who discontinue from the study for any reason will complete the EOT visit, and the follow-up safety visit (18 weeks after last dose).