Ye'elimite is the principal component in calcium sulfoaluminate cement, which currently attracts significant attention, since it can be produced with lower CO₂ emissions compared to conventional portland cement. The crystal structure of ye'elimite is not well-established, and it has been proposed to exhibit cubic, tetragonal, and orthorhombic structures. The present work reports a comprehensive ²⁷Al magic-angle spinning (MAS) and multiple-quantum (MQ) MAS NMR study of ye'elimite, utilizing six magnetic fields from 4.7 to 22.3 T. These spectra are only compatible with the orthorhombic Pcc2 structure of ye'elimite, implying the presence of eight distinct AlO₄ sites. The ²⁷Al NMR spectra are convincingly simulated by eight distinct sites, and ²⁷Al quadrupole coupling parameters and isotropic chemical shifts are reported for the first time for ye'elimite. These parameters are a prerequisite for a reliable interpretation and quantification of ye'elimite in ²⁷Al NMR spectra of ye'elimite-based cements. Density functional theory (DFT) calculations are used in the assignment of the specific Al sites in ye'elimite. Structural relaxations by DFT, using two proposed Pcc2 structures as starting points, result virtually in the same set of optimized fractional atomic coordinates, which is proposed as a new refined structure for ye'elimite. The refined structure gives the best agreement between experimental and calculated ²⁷Al quadrupole tensor elements for the eight Al sites. Finally, the ³³S MAS NMR spectra for ye'elimite, monosulfate, and anhydrite are reported.