Digital pharmacy algorithms are governed through legal, regulatory, organizational, commercial, professional, and patient-facing arrangements. These arrangements distribute authority unevenly and often separate formal accountability from practical control. To integrate evidence on who governs medication-related algorithms, where responsibilities arise across the lifecycle, and how monitoring, challenge, correction, and redress are allocated. An integrative review combined health, pharmacy, informatics, policy, ethical, and legal scholarship published from 2017 through 2026. Searches covered MEDLINE, Scopus, Web of Science Core Collection, International Pharmaceutical Abstracts, HeinOnline, and citation searching. Eligible peer-reviewed reports had to identify a governance actor, authority, responsibility, mechanism, or lifecycle stage relevant to digital pharmacy or medication-related algorithms. Records were deduplicated, screened, retrieved, appraised by source type, extracted into a structured governance framework, and synthesized through comparative thematic analysis. The search identified 556 records; 214 duplicates were removed, 342 records were screened, 68 reports were sought, 3 were not retrieved, and 65 full texts were assessed. Thirty reports representing 30 studies or scholarly analyses were included. Governance was distributed across regulators, healthcare organizations, vendors, developers, pharmacists, and patients, but the allocation of monitoring, incident investigation, correction, and redress was inconsistent. Formal regulatory authority did not reliably correspond to operational control. Pharmacists retained professional duties, while vendors and organizations controlled many technical and workflow conditions. Patient participation and contestability remained underdeveloped. Digital pharmacy algorithm governance is multilevel, fragmented, and lifecycle-dependent. Clearer allocation of authority, documentation, surveillance, escalation, and redress is needed before governance arrangements can be considered dependable.