This paper introduces Web3DB, a decentralized relational database management system (RDBMS) designed to align with the principles of Web 3.0, addressing critical shortcomings of traditional centralized DBMS, such as data privacy, security vulnerabilities, and single points of failure. Several similar systems have been proposed, but they are not compatible with the legacy systems based on RDBMS. Motivated by the necessity for enhanced data sovereignty and the decentralization of data control, Web3DB leverages blockchain technology for fine-grained access control and utilizes decentralized data storage. This system leverages a novel, modular architecture that contributes to enhanced flexibility, scalability, and user-centric functionality. Central to the Web3DB innovation is its decentralized query execution, which uses cryptographic sortition and blockchain verification to ensure secure and fair query processing across network nodes. The motivation for integrating relational databases within decentralized DBMS primarily stems from the need to combine the robustness and ease of use of relational database structures with the benefits of decentralization. This paper outlines the architecture of Web3DB, its practical implementation, and the system's ability to support SQL-like operations on relational data, manage multi-tenancy, and facilitate open data sharing, setting new standards for decentralized databases in the Web 3.0 era.