This article presents a comprehensive, theoretically grounded framework for secure, cost-optimal, and integrity-preserving migration of enterprise data from proprietary relational database management systems (RDBMS) such as Oracle to open-source cloud-native platforms such as PostgreSQL. We synthesize insights from contemporary research in cloud data security, cost-aware migration strategies, data integrity verification, multi-cloud placement optimization, master data management, and cryptographic key exchange to construct an end-to-end methodology suitable for large-scale enterprise modernization projects. The framework addresses the three core tensions enterprises face during migration: (1) maintaining confidentiality, integrity, and availability while data moves across trust boundaries (security tension); (2) minimizing total cost of ownership and operational expenditure without sacrificing performance or regulatory compliance (cost tension); and (3) assuring semantic correctness—schema, stored-procedure, and business-logic fidelity—when translating proprietary constructs into open-source equivalents (semantic tension). The article provides a rigorous description of preparatory assessment, hybrid migration staging, verification and auditing techniques, workload-aware cost modeling, and long-term operational governance. We further analyze potential failure modes, adversarial threats, and practical limitations, and propose mitigation strategies including cryptographic auditing, incremental migration scheduling, schema refactoring heuristics, and master data harmonization controls. This contribution integrates prior empirical studies and theoretical models into a unified narrative and offers a prescriptive roadmap for researchers, system architects, and enterprise engineers seeking to modernize database infrastructure while preserving security, cost-effectiveness, and trustworthiness.