In this paper, we present a novel approach to overcome challenges in the initial conception, design and implementation of Digital Twins. By applying established Model-Based System Engineering (MBSE) methods, we have developed a tool to automatically generate Digital Twins from an existing system model. In contrast to conventional approaches, which are often based on error-prone manual creation, our approach offers a systematic, model-based solution. To demonstrate the feasibility of this approach, we present a prototype implementation that is able to generate Digital Twins directly from an available MBSE model, which in turn enables seamless integration and reuse of existing model structures. This not only simplifies the creation process of Digital Twins, but also improves scalability and maintainability by reusing existing MBSE models to transform the already specified systems into Digital Twins. In our application prototype, we demonstrate this methodology using a simplified satellite system as an example of a system that is automatically converted into a usable Digital Twin Instance. The integration of MBSE principles into the design process not only increases the accuracy and reliability of the generated Digital Twins, but also facilitates their alignment with the intended operational processes and the requirements placed on the physical system they represent.