Major maritime carriers are globally demanding improvements in the efficiency of port operations. Cargo carried by ships must be loaded and unloaded quickly with minimal stopover time in the port. This requirement mandates seaports to deploy cutting-edge technology to the port area so that logistic processes are increasingly efficient and reliable. In this scenario, the attack surface of such critical infrastructure is growing very rapidly and advanced security techniques must be deployed to enforce a high attack resilience. A Distributed Ledger-based Credential Management System exploiting a Distributed Ledger Technology (DLT) to enable transparent and real-time tracking of logistic vehicles and cargos within a terminal is presented in this paper. Based on a customization of Vehicular Ad-Hoc Network (VANET) security standards, the proposed scheme provides authentication, authorization, and revocation capabilities to promptly exclude misbehaving logistic vehicles from the system, while maintaining an immutable record of all the logistic vehicles' activity. The laboratory validation demonstrates that the delay of the devised scheme is not dependent on the quay area capacity, thus being applicable in seaports of any size. Furthermore, the effectiveness of the solution is demonstrated with the field trial results obtained with the EU Horizon 2020 COREALIS project testbed deployed in the Port of Livorno.