Implementing federated learning (FL) within the Internet of Everything (IoE) framework poses substantial computational challenges, stemming from extensive client involvement, which can lead to escalated training expenses and diminished convergence rates. While many studies have investigated the combination of FL and blockchain networks, the integration of public and private chains to enhance FL performance remains largely unexplored. In this study, we introduce an innovative methodology that unifies public and private chains to mitigate clients’ computational demands while preserving data privacy and security, demonstrating compatibility within the IoE milieu and yielding favorable outcomes. To facilitate secure model migration and expedite training without incurring excessive computation costs, we delineate a blockchain-anchored model migration scheme tailored for resource-limited Internet of Things infrastructures, establishing a private chain mechanism to incentivize companies possessing multiple devices or clients to prioritize model training. Employing blockchain technology guarantees trustworthiness in model migration, precluding the disclosure of devices’ confidential data. Overall, our innovative method provides an effective solution that improves the accuracy, privacy, and security of FL while reducing clients’ computational burdens within the context of the IoE.