This article presents a comprehensive framework for applying blockchain technology to secure data integration challenges in multi-cloud and hybrid-cloud environments. This article examines how distributed ledger technology creates a trust layer that addresses key vulnerabilities in traditional integration approaches while maintaining performance characteristics suitable for enterprise deployments. This article's architecture leverages permissioned blockchain networks, smart contracts, and cryptographic verification mechanisms to ensure data integrity, enforce governance policies, and provide immutable audit trails across heterogeneous cloud platforms. Our performance evaluation demonstrates viable throughput and latency characteristics compared to traditional integration methods, while offering enhanced security properties. Through case studies in financial services, healthcare, supply chain, and critical infrastructure protection, we illustrate practical implementations and quantifiable benefits. Despite challenges in scalability, energy consumption, legacy system integration, regulatory compliance, and organizational adoption, the architecture shows promising results for high-value data workflows. The research contributes to the emerging intersection of blockchain and multi-cloud computing by providing both theoretical foundations and practical implementation guidance for organizations seeking to enhance security posture across distributed cloud environments.