Subscriber authentication is a primitive operation in mobile networks required by each operator prior to offering any service to end users. In this paper, we propose a novel blockchain-based Authentication and Key Agreement (AKA) protocol for roaming services in 5G networks. Each Home Network (HN) creates its own smart contract and publishes its address to inform other operators who want to offer roaming services to HN subscribers. All subsequent communication between the HN and Serving Network (SN) is done by calling the function of this smart contract. The proposed protocol eliminates the need for a secure channel between the HN and SN, which is a primary requirement of current 5G AKA protocols. In practice, a secure channel requires the HN and SN to establish a secure session before running the AKA protocol. Further, the proposed protocol leverages the benefits of blockchain, such as auditable log, decentralized architecture, and the prevention of Denial of Service (DoS) attacks. Furthermore, we provide a security proof of the protocol through formal verification using ProVerif. The results show that our scheme tends to preserve user privacy and at the same time provides mutual authentication of the participants. Finally, our evaluation of the Ethereum blockchain shows that the protocol is efficient in terms of both transaction and execution costs.