Long-Term Evolution/Long-Term Evolution Advanced (LTE/LTE-A) is the latest mobile communication technology that is offering high data rates and robust performance to the subscribers. Since LTE/ LTE-A standards are established on the Internet Protocol (IP) connectivity and provide compatibility with the heterogeneous networks, these new features create availability of the new security challenges in the LTE/LTE-A networks. Taking into consideration the issues of serious signalling congestion and security loopholes in LTE/ LTE-A networks, the authors propose an Efficient Authentication and Key Agreement Protocol for Evolved Packet System (EAKA-EPS) with secure handover procedures. The proposed protocol achieves outstanding results in terms of the optimization of computation and signalling overhead. With this, the protocol guarantees the needed security requirements like protected wireless interface and strong mutual authentication between the entities, and ensures access stratum secrecy at the time of handovers. The formal verification results of the proposed scheme over the security verification and simulation tool ''Automated Validation of Internet Security Protocols and Applications (AVISPA)'' show that the suggested protocol is safe against various malicious attacks, which are still possible in LTE/LTE-A networks. To the best of the authors' knowledge, the suggested approach is the first approach that provides perfect secrecy with less computation and communication overhead in the LTE/LTE-A networks.