Inclusion Criteria:

• Is male or female with Ulcerative Colitis or Crohn's Disease and was between 2 to 17 years, inclusive, at the time of randomization for Study MLN0002-2003. (Note: A participant remains eligible to participate in this study after they reach 18 years of age if they continue to meet the inclusion criteria and do not meet any exclusion criteria).
• Has completed Study MLN0002-2003 and, at Week 22, achieved clinical response as defined by a reduction of partial Mayo score of >= 2 points and >= 25% from Baseline, or a reduction of the paediatric ulcerative colitis activity index (PUCAI) of >= 20 points from baseline for participants with UC; or a reduction of the CDAI as defined by a >= 70-point decrease from Baseline or a decrease of pediatric crohn's disease activity index (PCDAI) of >= 15 points for participants with CD.
• May be receiving a therapeutic dose of the following drugs:
  • Oral 5-aminosalicylic acid (5-ASA) compounds;
  • Oral corticosteroid therapy (prednisone or equivalent steroid at a dose less than or equal to [<=] 50 milligram per day [mg/day], budesonide at a dose <= 9 mg/day);
  • Topical (rectal) treatment with 5-ASAs or corticosteroids;
  • Probiotics (example, Saccharomyces boulardii);
  • Antidiarrheals (example, loperamide, diphenoxylate with atropine) for control of chronic diarrhea;
  • Antibiotics used for the treatment of CD (i.e., ciprofloxacin, metronidazole);
  • Azathioprine (AZA) or 6-mercaptopurine (6-MP) or methotrexate (MTX), provided the participant was receiving this medication during prior participation in MLN0002-2003.
• 4. The participant's vaccinations are up to date as per inclusion criteria number 10 in MLN0002-2003.

Exclusion Criteria:

• Is female and is lactating or pregnant.
• Has hypersensitivity or allergies to vedolizumab or any of its excipients.
• Has withdrawn from Study MLN0002-2003.
• Has developed any new unstable or uncontrolled cardiovascular, heart failure moderate to severe (New York Class Association III or IV), pulmonary, hepatic, renal, gastrointestinal (GI), genitourinary, hematological, coagulation, immunological, endocrine/metabolic, neurological, or other medical disorder that, in the opinion of the investigator, would confound the study results or compromise participant safety.
• Has a positive progressive multifocal leukoencephalopathy (PML) subjective symptom checklist prior to the administration of the first dose of study drug.
• Currently requires major surgical intervention for ulcerative colitis (UC) or CD (example, bowel resection), or is anticipated to require major surgical intervention for UC or CD during the study.
• Has other serious comorbidities that will limit his or her ability to complete the study.