In 2015, the development of the conceptual design of IGNITOR, a Russian–Italian experimental thermonuclear tokamak, was completed, and the parameters of all the systems, including the fuel system, were determined. In this work, an integrated design of arrangement of all the tritium-containing gas and secondary water streams expected in the operation of the IGNITOR tokamak was proposed on the basis of analyzing the designs of the fuel cycles of the large thermonuclear facilities JET, TFTR, and ITER. This design includes the storage of deuterium and tritium in a system of gas cylinders at a pressure of 0.4 MPa, the purification of the exhaust gas mixture from the plasma chamber using a “hot getter,” the separation of the deuterium–tritium isotope mixture by displacement gas chromatography, the purification of the process gas and air streams in a wet scrubber, and the detritiation of the water streams by chemical isotope exchange of hydrogen with water. The main technical parameters of equipment in the proposed design were estimated.