The Search for Hidden Particles (SHiP) experiment proposal at CERN demands a dedicated dipole magnet for its scattering and neutrino detector. This requires a very large volume to be uniformly magnetized at B > 1.2 T, with constraints regarding the inner instrumented volume as well as the external region, where no massive structures are allowed and only an extremely low stray field is admitted. In this paper we report the main technical challenges and the relevant design options providing a comprehensive design for the magnet of the SHiP Scattering and Neutrino Detector.