This thesis work presents an architectural design of a system to bring non-repudiation concept into the IP based digital voice conversations (VoIP) in LTE and UMTS networks, using electronic signatures, by considering a centralized approach. Moreover, functionalities and technical methods to support such a system are researched. Last but not least, ways to introduce this system as a public and commercial service are discussed. Non-repudiation concept provided by electronic signatures and related cryptographic functions, as introduced in this study, allow using digital records of these voice conversations as legally binding statements or proofs likewise and even instead of traditional wet signatures. The system is designed as a subsystem to IMS based 3G and 4G networks and maximum compatibility with current configurations, components and interfaces of these networks is intended. On the other hand non-repudiation is achieved by special signature, storage and verification units located in the IMS core network. Voice data is proposed to be processed in MRF unit of the IMS. Additionally, a USSD/USSI based special solution to initiate these signed calls is developed. According to the proposed scheme; during a signed call, two unidirectional voice streams originating from two parties of the call, which are transferred in IP and UDP encapsulated RTP packages, are received by the signature unit and interweaved using their arrival times, so that they become a unified stream. Signature unit generates hashes of groups of received packages and signs them using PKI algorithms and applying hash/signature chaining to increase integrity protection and to empower non-repudiation. Then, it forwards packages and signature information to the storage unit. Storage unit keeps all the call records, signature data and metadata of these calls. Verification unit later gathers relevant data from the storage unit...