A theoretical study of geometrical structures, electronic properties, and spectral properties of single-atom transition metal-doped boron clusters MB₂₄⁻ (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) is performed using the CALYPSO approach for the global minimum search, followed by density functional theory calculations. The global minima obtained for the MB₂₄⁻ (M = Sc, Ti, V, and Cr) clusters correspond to cage structures, and the MB₂₄⁻ (M = Mn, Fe, and Co) clusters have similar distorted four-ring tubes with six boron atoms each. Interestingly, the global minima obtained for the NiB₂₄⁻ cluster tend to a quasi-planar structure. Charge population analyses and valence electron density analyses reveal that almost one electron on the transition-metal atoms transfers to the boron atoms. The electron localization function (ELF) of MB₂₄⁻ (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) indicates that the local delocalization of MB₂₄⁻ (M = Sc, Ti, V, Cr, and Ni) is weaker than that of MB₂₄⁻ (M = Mn, Fe, and Co), and there is no obvious covalent bond between doped metal and B atoms. The spin density and spin population analyses reveal that open-shell MB₂₄⁻ (M = Ti, Cr, Fe, and Ni) has different spin characteristics which are expected to lead to interesting magnetic properties and potential applications in molecular devices. The polarizability of MB₂₄⁻ (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) shows that MB₂₄⁻ (M = Mn, Fe, and Co) has larger first hyperpolarizability, indicating that MB₂₄⁻ (M = Mn, Fe, and Co) has a strong nonlinear optical response. Hence, MB₂₄⁻ (M = Mn, Fe, and Co) might be considered as a promising nonlinear optical boron-based nanomaterial. The calculated spectra indicate that MB₂₄⁻ (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) has different and meaningful characteristic peaks that can be compared with future experimental values and provide a theoretical basis for the identification and confirmation of these single-atom transition metal-doped boron clusters. Our work enriches the database of geometrical structures of doped boron clusters and can provide an insight into new doped boron clusters.