Vedolizumab IV in Pediatric Participants With Ulcerative Colitis (UC) or Crohn's Disease (CD)

The drug being tested in this study is called vedolizumab. Vedolizumab is being tested to treat pediatric participants who have moderately to severely active UC or CD. This study will look at the PK, efficacy, immunogenicity, safety, and tolerability in participants who take vedolizumab. The study will enroll approximately 80 participants. Participants will be randomly assigned (by chance, like flipping a coin) to one of the two dose regimens (high or low) per weight group \>=30 kg and 10 kg to \<30 kg in ratio 1:1-which will remain undisclosed to the participant and study doctor during the study (unless there is an urgent medical need): * Vedolizumab high dose group - Vedolizumab 300 mg or 200 mg * Vedolizumab low dose group - Vedolizumab 150 mg or 100 mg All participants will be administered vedolizumab via IV infusion. Participants assigned to the low dose group who do not achieve clinical response (based on pediatric UC/CDAI) at Week 14 will receive the high dose (that is, 300 mg for participants \>=30 kg baseline weight and 200 mg for participants 10 kg to \<30 kg baseline weight) of vedolizumab IV at Week 14. Participants assigned to the high dose group who had not achieved clinical response continued on the same blinded high dose at Week 14. This multi-center trial will be conducted worldwide. The overall time to participate in this study is up to 36 weeks. After completing the Week 22 Visit procedures, eligible participants may enter a blinded extension study. Participants will make multiple visits to the clinic, and those who do not enter extension study will have a final visit 18 weeks after last dose of study drug for a follow-up assessment. Participants who do not enter the extension study will also participate in a long-term safety follow-up, by telephone, 6 months after the last dose of study drug.