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Federated Learning (FL) has emerged as a transformative distributed learning paradigm in the era of Internet of Things (IoT), reconceptualizing data processing methodologies. However, FL systems face significant communication bottlenecks due to inevitable client-server data exchanges and long-distance transmissions. This work presents EdgeFLow, an innovative FL framework that redesigns the system topology by replacing traditional cloud servers with sequential model migration between edge base stations. By conducting model aggregation and propagation exclusively at edge clusters, EdgeFLow eliminates cloud-based transmissions and substantially reduces global communication overhead. We provide rigorous convergence analysis for EdgeFLow under non-convex objectives and non-IID data distributions, extending classical FL convergence theory. Experimental results across various configurations validate the theoretical analysis, demonstrating that EdgeFLow achieves comparable accuracy improvements while significantly reducing communication costs. As a systemic architectural innovation for communication-efficient FL, EdgeFLow establishes a foundational framework for future developments in IoT and edge-network learning systems.