This research study is evaluating an investigational treatment called vedolizumab for moderately to severely active ulcerative colitis (UC) or Crohn's Disease (CD) in children. The purpose of this study is to find out how vedolizumab is processed by the bodies of children with moderately to severely active UC or CD, test to see whether the body makes antibodies against vedolizumab, test how safe vedolizumab is in children, and find out how vedolizumab may affect quality of life and growth and puberty.

Vedolizumab has been tested previously in adults (18 years or older) for UC and CD treatment and has shown satisfactory results in multiple completed clinical trials (studies in people 18 years or older). Vedolizumab was also previously tested in the pediatric (children) population. However, there are still limited results available for the use of vedolizumab in children. Therefore, its use in this study is considered investigational, which means that it has not been approved by the U.S. Food and Drug Administration (FDA) for the treatment of children. Vedolizumab (intravenous) has been approved for the treatment of UC or CD for adults and vedolizumab (subcutaneous) has been approved for maintenance treatment of UC or CD in adults.

Vedolizumab belongs to a group of proteins called antibodies, which help reduce inflammation that can cause the symptoms (frequent bowel movements, and bleeding from the rectum) of UC and CD. Participants will receive vedolizumab through an IV (a slow injection in the vein) during the Induction Period of the study. The induction dose will be given at Day 1, Week 2, and Week 6 of the study. The amount of study drug that each participant will receive will be dependent upon their weight at screening.

After the Induction Period, participants will move on to the Maintenance Period of the study. During the Maintenance Period, participants will receive the study drug through a subcutaneous (SC) injection (an injection under the skin). The study drug will be given either every two weeks beginning at Week 14 through Week 34 or every four weeks from Week 14 to Week 30 depending on each participant's weight. For the first SC dose, participants will need to be monitored at the study site for 30 to 60 minutes. If there are no signs of an allergic reaction for the first SC dose, the time needed to monitor for each later SC dose may be 15 to 30 minutes.

All participants will be asked to attend study visits and provide blood and fecal samples. There will also be one colonoscopy and there may be an additional optional colonoscopy and a physical exam.

Total study participation will last up to 13 months.