Inclusion Criteria:

1. Is male or female with UC or CD 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.)

1. Oral 5-aminosalicylic acid (5-ASA) compounds.
2. Oral corticosteroid therapy (prednisone or equivalent steroid at a dose less than or equal to [<=] 50 milligram per day [mg/day]) provided the participant was receiving this medication during prior participation in MLN0002-2003.
3. Topical (rectal) treatment with 5-ASA or corticosteroids.
4. Probiotics (example, Saccharomyces boulardii).
5. Antidiarrheals (example, loperamide, diphenoxylate with atropine) for control of chronic diarrhea.
6. Antibiotics used for the treatment of CD (i.e., ciprofloxacin, metronidazole).
7. 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:

1. Is female and is lactating or pregnant.
2. Has hypersensitivity or allergies to vedolizumab or any of its excipients.
3. Has withdrawn from Study MLN0002-2003.
4. 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.
5. Has a positive progressive multifocal leukoencephalopathy (PML) subjective symptom checklist prior to the administration of the first dose of study drug.
6. Currently requires major surgical intervention for UC or CD (example, bowel resection), or is anticipated to require major surgical intervention for UC or CD during the study.
7. Has other serious comorbidities that will limit his or her ability to complete the study.