Hadron therapy refers to a medical treatment that uses hadron beams (i.e. protons and ions) to deliver localized energy that suppresses cancerous cells, sparing the neighbouring healthy tissues from unwanted radiation. The major technical components of a hadron therapy centre are the particle accelerator (cyclotron, synchrotron, or linac) and the beam delivery system that controls, shapes and orients the particles towards the area to be treated. The beam delivery can consist of fixed transfer lines, or it can include a gantry, a transfer line that rotates around the patient and allows radiation from multiple directions. The present work investigates a new toroidal gantry for hadron therapy, named GaToroid. This novel gantry configuration allows the dose delivery from a discrete number of angles avoiding magnets as well as patient rotation. Compared to traditional gantries that require rotating magnets, this improvement is made possible by a toroidal magnet operating in steady-state. This design constitutes the ideal conditions for the use of superconductors to generate a significantly higher magnetic field compared to normal-conducting solutions, as well as to reduce the weight and footprint of the magnets. The study of a GaToroid system requires the integration of several aspects of physics and engineering. In this framework, the focus of this research is on the design of the superconducting coils integrated with beam optics and particle tracking analyses. The first part of the thesis illustrates the optimization of the toroidal magnet. Coupling two-dimensional particle tracking and magnetic field calculations, an algorithm was developed to identify optimal gantry configurations that maximize the energy acceptance of the system. Two solutions composed of 16 coils, differing in high and low values of engineering current density, were investigated. In line with current clinical requirements, the beams converged at the isocenter within 1 mm over the whole treatment energy spectrum for both configurations. The second part of the thesis describes the algorithm implemented for the two- and three-dimensional particle tracking. Building upon the results of the magnetic optimization, a linear beam optics formalism was developed to determine the focusing properties of GaToroid. The third part of the thesis focuses on the engineering design of the low current density solution. Using two thermo-electric models, lumped and one-dimensional, the Nb-Ti and ReBCO cable geometries were validated, together with the quench protection system. Furthermore, analytical and numerical studies on mechanics made it possible to estimate the overall footprint and weight of the system. Results show that, compared with the state-of-the-art gantries, the proposed GaToroid solution has the potential to be more compact and lighter by at least a factor two. Finally, the last part of the thesis describes the design of a scaled-down demonstrator wound with ReBCO tapes. Studies on quench protection, mechanics and experimental implementation aimed at testing the use of ReBCO technology for GaToroid coils are discussed. In conclusion, this work presents the first overall description of a GaToroid system, ranging from the analytical definition, magnetic optimization, particle tracking and magnet engineering. The investigation of this new toroidal paradigm for gantries represents a quantum step toward more compact and less expensive solutions for hadron therapy centres.