The magnet feeders are part of the critical systems of a fusion reactor since they represent the interface between the in-cryostat components at 4.5 K and the room-temperature cryogenic plant and power supply. The European DEMO tokamak foresees 16 toroidal field (TF) coil feeders, 5 central solenoid (CS) feeders and 6 poloidal field (PF) coil feeders, which must be routed inside the galleries of the tokamak building. By realising the required electrical and cryogenic connections, the mechanical supports and casing, as well as hosting instrumentation cables, the feeders ensure the safe operation of the superconducting magnets. Therefore, the design and integration study of the magnet feeders is one of the key activities within the conceptual design phase of the European DEMO. Despite several preliminary studies have been performed, a systematic overview on the magnet feeder system is still missing. In this work, we report recent progress in the design of the magnet feeders, starting from the outline design of the superconducting bus bars and current leads, which connect the room-temperature power supply bus bars to the coils at about 4.5 K. Further design activities have been started on the integration of the feeder structures within the tokamak building, considering also the positioning of additional cryogenic and electrical modules, as well as on the thermal-structural design of feeder components. The process flow diagram of the feeders for the toroidal field coils has been also introduced, with a particular focus on the operation of the cryogenic lines at different temperature and pressure levels. This work is a relevant step for advancing the design of the whole European DEMO fusion reactor, representing a relevant starting point for future engineering design activities and industrial studies.