Formation flying is commonly identified as the collective usage of two or more cooperative spacecraft to exercise the function of a single monolithic virtual instrument. The distribution of tasks and payloads among fleets of coordinated smaller satellites offers the possibility to overcome the classical limitations of traditional single-satellite systems. The science return is enhanced through observations made with larger, configurable baselines and an improved degree of redundancy can be achieved in the event of failures. Different classes of formation flying missions are currently under discussion within the engineering and science community: technology demonstration missions, synthetic aperture interferometers and gravimeters for Earth observation, multi-spacecraft interferometers in the infrared and visible wavelength regions as a key to new astrophysics discoveries and to the direct search for terrestrial exoplanets. These missions are characterized by different levels of complexity, mainly dictated by the payload metrology and actuation needs, and require a high level of on-board autonomy to satisfy the continuously increasing demand of relative navigation and control accuracy. This dissertation presents the first realistic demonstration of a complete guidance, navigation and control (GNC) system for formation flying spacecraft in low Earth orbit. Numerous technical contributions have been made during the course of this research in the areas of formation flying guidance, GPS-based relative navigation, and impulsive relative orbit control, but the primary contribution of this thesis does not lie in one or more of these disciplines. The innovation and originality of this work stems from the design and implementation of a comprehensive formation flying system through the successful integration of various techniques. This research has led to the full development, testing and validation of the GNC flight code to be embedded in the on-board computer of the active spacecraft of the PRISMA technology demonstration. Furthermore key guidance and control algorithms presented here are going to be demonstrated for the first time in the TanDEM-X formation flying mission. Overall this thesis focuses on realistic application cases closely related to upcoming missions. The intention is to realize a practical and reliable way to formation flying: a technology that is discussed and studied since decades but is still confined in research laboratories. Hardware-in-the-loop real-time simulations including a representative flight computer and the GPS hardware architecture show that simple techniques, which exploit the natural orbit motion to full extent, can meet the demanding requirements of long-term close formation-flying.