Cloud computing, as the most widely applied and prominent domain of distributed systems, has brought numerous advantages to users, including high resource sharing efficiency, strong availability, and excellent scalability. However, the complexity of cloud computing environments also introduces various risks and challenges. In the current landscape with numerous cloud service providers and diverse hardware configurations in cloud environments, addressing challenges such as establishing trust chains, achieving general-purpose virtual remote attestation, and ensuring secure virtual machine migration becomes a crucial issue that traditional remote attestation architectures cannot adequately handle. Confronted with these issues in a heterogeneous multi-cloud environment, we present a targeted solution—a secure migration-enabled generic virtual remote attestation architecture based on improved TEE. We introduce a hardware trusted module to establish and bind with a Virtual Root of Trust (VRoT), addressing the challenge of trust chain establishment. Simultaneously, our architecture utilizes the VRoT within TEE to realize a general-purpose virtual remote attestation solution across heterogeneous hardware configurations. Furthermore, we design a controller deployed in the trusted domain to verify migration conditions, facilitate key exchange, and manage the migration process, ensuring the security and integrity of virtual machine migration. Lastly, we conduct rigorous experiments to measure the overhead and performance of our proposed remote attestation scheme and virtual machine secure migration process. The results unequivocally demonstrate that our architecture provides better generality and migration security with only marginal overhead compared to other traditional remote attestation solutions.