Intelligent Transportation has seen significant advancements with Deep Learning and the Internet of Things, making Traffic Signal Control (TSC) research crucial for reducing congestion, travel time, emissions, and energy consumption. Reinforcement Learning (RL) has emerged as the primary method for TSC, but centralized learning poses communication and computing challenges, while distributed learning struggles to adapt across intersections. This paper presents a novel approach using Federated Learning (FL)-based RL for TSC. FL integrates knowledge from local agents into a global model, overcoming intersection variations with a unified agent state structure. To endow the model with the capacity to globally represent the TSC task while preserving the distinctive feature information inherent to each intersection, a segment of the RL neural network is aggregated to the cloud, and the remaining layers undergo fine-tuning upon convergence of the model training process. Extensive experiments demonstrate reduced queuing and waiting times globally, and the successful scalability of the proposed model is validated on a real-world traffic network in Monaco, showing its potential for new intersections.