The adoption of agentic AI coding systems -- where autonomous agents generate, review, test, and deploy code with minimal human intervention -- creates a governance challenge in regulated industries. Existing frameworks address AI-assisted development maturity or the productivity-reliability tension but offer no mechanism for calibrating human oversight intensity to regulatory impact. We present the Governed AI-Assisted Engineering (GAIE) framework, a three-tier graduated human oversight model for agentic code generation in regulated domains. GAIE introduces the Oversight Classification Model (OCM), a deterministic decision function that classifies code generation tasks by regulatory impact, customer proximity, reversibility, and data sensitivity to route them through one of three oversight tiers: human-in-the-loop (strategic functions), human-over-the-loop (customer-impacting), or automated-with-monitoring (internal). Each tier defines required evidence artifacts for compliance auditability. We map GAIE against the Bank of Thailand's 2025 AI risk-management policy and demonstrate cross-jurisdiction applicability to MAS (Singapore), NIST AI RMF, ISO/IEC 42001, and the EU AI Act. Evaluation through regulatory coverage analysis, comparative framework analysis, and analytical productivity modeling suggests that graduated oversight preserves 84--97% of agentic coding velocity (central estimate: 91%) while maintaining compliance evidence coverage for regulated functions. GAIE contributes a framework that explicitly bridges AI-assisted development maturity with regulatory governance through proportionate human oversight.

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