With the increasing development of advanced communication technologies, vehicles are becoming smarter and more connected. Due to the tremendous growth of various vehicular applications, a huge amount of data is generated through advanced on-board devices and is deemed critical to improve driving safety and enhance vehicular services. However, cloud based models often fall short in applications where latency and mobility are critical. In order to fully realize the potential of vehicular networks, the challenges of efficient communication and computation need to be addressed. In this direction, vehicular fog computing (VFC) has emerged which extends the concept of fog computing to conventional vehicular networks. It is a geographically distributed paradigm that has the potential to conduct time-critical and data-intensive tasks by pushing intelligence (i.e. computing resources, storage, and application services) in the vicinity of end vehicles. However secure and reliable transmission are of significant importance in highly-mobile vehicular networks in order to ensure the optimal Quality of Service (QoS). In this direction, several authentication mechanisms have been proposed in the literature but most of them are found unfit due to absence of decentralization, anonymity, and trust characteristics. Thus, an effective cross-datacenter authentication and key-exchange scheme based on blockchain and elliptic curve cryptography (ECC) is proposed in this paper. Here, the distributed ledger of blockchain is used for maintaining the network information while the highly secure ECC is employed for mutual authentication between vehicles and road side units (RSUs). Additionally, the proposed scheme is lightweight and scalable for the considered VFC setup. The performance evaluation results against the existing state-of-the-art reveal that the proposed scheme accomplishes enhanced security features.