Precision farming has a positive potential in the agricultural industry regarding water conservation, increased productivity, better development of rural areas, and increased income. Blockchain technology is a better alternative for storing and sharing farm data as it is reliable, transparent, immutable, and decentralized. Remote monitoring of an agricultural field requires security systems to ensure that any sensitive information is exchanged only among authenticated entities in the network. To this end, we design an efficient blockchain-enabled authenticated key agreement scheme for mobile vehicles-assisted precision agricultural Internet of Things (IoT) networks called$AgroMobiBlock$. The limited existing work on authentication in agricultural networks shows passive usage of blockchains with very high costs.$AgroMobiBlock$proposes a novel idea using the elliptic curve operations on an active hybrid blockchain over mobile farming vehicles with low computation and communication costs. Formal and informal security analysis along with the formal security verification using the Automated Validation of Internet Security Protocols and Applications (AVISPA) software tool have shown the robustness of$AgroMobiBlock$against man-in-the-middle, impersonation, replay, physical capture, and ephemeral secret leakage attacks among other potential attacks. The blockchain-based simulation on large-scale nodes shows the computational time for an increase in the network and block sizes. Moreover, the real-time testbed experiments have been performed to show the practical usefulness of the proposed scheme.