With the integration of the Internet of Things (IoT) in the field of transportation, the Internet of Vehicles (IoV) turned to be a vital method for designing Smart Transportation Systems (STS). STS consist of various interconnected vehicles and transportation infrastructure exposed to cyber intrusion due to the broad usage of software and the initiation of wireless interfaces. This study proposes a federated deep learning-based intrusion detection framework (FED-IDS) to efficiently detect attacks by offloading the learning process from servers to distributed vehicular edge nodes. FED-IDS introduces a context-aware transformer network to learn spatial-temporal representations of vehicular traffic flows necessary for classifying different categories of attacks. Blockchain-managed federated training is presented to enable multiple edge nodes to offer secure, distributed, and reliable training without the need for centralized authority. In the blockchain, miners confirm the distributed local updates from participating vehicles to stop unreliable updates from being deposited on the blockchain. The experiments on two public datasets (i.e., Car-Hacking, TON_IoT) demonstrated the efficiency of FED-IDS against state-of-the-art approaches. It reveals the credibility of securing networks of intelligent transportation systems against cyber-attacks.