Intelligent Transportation has seen significant advancements with Deep Learning (DL) and 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. Additionally, the output layer's parameters are not aggregated to handle different intersection settings; instead, fine-tuning is performed after model training for deployment. Extensive experiments demonstrate reduced queuing and waiting times globally, and successful scalability of the proposed model is validated on a real-world traffic network in Monaco, showing its potential for new intersections.