Due to the distance limitation of quantum communication via ground-based fibre networks, space-based quantum key distribution (QKD) is a viable solution to extend such networks over continental and, ultimately, over global distances. Compared to Low Earth Orbits (LEO), QKD from a Geostationary Orbit (GEO) offers substantial advantages, such as large coverage, continuous link to ground stations (cloud cover limited), 24/7 operation (background limited), and no tracking required. As a downside, QKD from GEO comes with large link losses due to the space-ground distance, lowering the achievable key rates. From our feasibility and conceptual design study it is concluded that although link losses are high, QKD from GEO is technically feasible, and a favourable solution if the satellite needs to act as an untrusted node (that is, no security assumptions required for the space segment). However, the optimal solution, generating a higher value-for-money, is to have the possibility to operate it in trusted mode as well, as higher key rates can be obtained. But this will be at the cost of security as key material needs to be (temporarily) stored on board of the satellite. In order to arrive at a minimum required secure bit rate of ~1 bit/s in untrusted mode, two ~0.5m diameter telescopes in the space segment are required with <0.65μrad pointing accuracy each, a >1GHz entangled photon pair generation rate, in combination with ~2.5m diameter telescopes on ground, operating at 810nm wavelength. In trusted mode, with the same optical system but only using one telescope in the space segment, a factor of ~300 to ~10000 more key can be obtained. Details on our assumptions and results and drawings of the high level system design are presented, as well as a description of the required technology improvements and building blocks needed, which is applicable to non-GEO applications as well.