A Continuation Study of TAK-279 in Adults With Ulcerative Colitis (UC) and Crohn's Disease (CD)

Inclusion Criteria: 1. The participant is willing and able to understand and fully comply with trial procedures and requirements (including digital tools and applications), in the opinion of the investigator. The participant has provided informed consent (that is, in writing, documented via a signed and dated informed consent form \[ICF\]) and any required privacy authorization prior to the initiation of any trial procedures. 2. Completion of Week 52 in the parent trials (phase 2b CD and phase 2 UC) with valid electronic (e) Diary data for Week 52 (TAK-279-CD-2001 and TAK-279-UC-2001). 3. Clinical or symptomatic responder at parent trial Week 52 as defined below: 1. TAK-279-CD-2001: Clinical response at Week 52 of the parent trial based on PRO2, assessed as \>=30% decrease in average daily very soft or liquid stools and/ or \>=30% decrease in average AP from parent trial baseline. 2. TAK-279-UC-2001: Symptomatic response at Week 52 of the parent trial, assessed as a reduction in partial modified Mayo score (pmMS) of \>=1 points and \>=30% from parent trial baseline; and a decrease from parent trial baseline in the rectal bleeding sub-score of \>=1 point or an absolute rectal bleeding sub-score of \<=1 point. 4. TAK-279-CD-2003: Endoscopic response at Week 12 of the parent trial, assessed as a participant achieving decrease in SES-CD \>50% from baseline (or for participants with isolated ileal disease, SES-CD \<=4 or at least a 2-point reduction from baseline). Other General Inclusion Criteria: 5. Participants must meet the contraception recommendations. Exclusion Criteria: 1. Participant considered by the investigator to be unsuitable for the OLE trial due to their trial compliance and medication adherence concerns. 2. Participants with malignancy or dysplasia per endoscopy any time during the parent trial or at the beginning of the OLE. Exclusion Criteria related to Laboratory Investigations: 3. Participants meeting the exclusion criteria related to laboratory investigations as defined in the protocol. Exclusion criteria related to other prohibited concomitant medication for TAK-279-CD-2001 and TAK-279-UC-2001 Cohorts: 4. Participants taking oral corticosteroids for CD or UC during parent trial at or after Week 48.