Edge caching is an emerging technology for addressing massive content access in mobile networks to support rapidly growing Internet-of-Things (IoT) services and applications. However, most current optimization-based methods lack a self-adaptive ability in dynamic environments. To tackle these challenges, current learning-based approaches are generally proposed in a centralized way. However, network resources may be overconsumed during the training and data transmission process. To address the complex and dynamic control issues, we propose a federated deep-reinforcement-learning-based cooperative edge caching (FADE) framework. FADE enables base stations (BSs) to cooperatively learn a shared predictive model by considering the first-round training parameters of the BSs as the initial input of the local training, and then uploads near-optimal local parameters to the BSs to participate in the next round of global training. Furthermore, we prove the expectation convergence of FADE. Trace-driven simulation results demonstrate the effectiveness of the proposed FADE framework on reducing the performance loss and average delay, offloading backhaul traffic, and improving the hit rate.