Abstract: This paper presents the design of a total absorption gamma-ray spectrometer for the determination of beta-decay intensity distributions of exotic nuclear species at the focal plane of the FAIR-NUSTAR Super Fragment Separator. The spectrometer is a key instrument in the DESPEC experiment and the proposed implementation follows extensive design studies and prototype tests. Two options were contemplated, based on Nal(TI) and LaBr3:Ce inorganic scintillation crystals respectively. Monte Carlo simulations and technical considerations determined the optimal configurations consisting of sixteen 15 x 15 x 25 cm(3) crystals for the Nal(Tl) option and one hundred and twenty-eight 5.5 x 5.5 x 11 cm(3) crystals for the LaBr3:Ce option. Minimization of dead material was crucial for maximizing the spectrometer full-energy peak efficiency. Module prototypes were build to verify constructional details and characterize their performance. The measured energy and timing resolution was found to agree rather well with estimates based on simulations of scintillation light transport and collection. The neutron sensitivity of the spectrometer, important when measuring beta-delayed neutron emitters, was investigated by means of Monte Carlo simulations.