This paper presents Governance-as-Code (GaC), a framework for translating the EU AI Act's technical requirements into executable compliance pipelines for generative AI systems. GaC addresses seven technical gaps in the Act's existing requirements, including data governance and human oversight. It provides a machine-checkable acceptance criteria framework with six compliance modules and a Rego policy code implementation. The authors validate GaC on two enterprise deployments, demonstrating a 75% reduction in audit labor compared to manual expert audits.