The study of double perovskite structures Ba2XSbO6 (X = Sc, Y) is carried out using the first principles algorithms within the framework of Density Functional Theory (DFT). The results showed that these compounds possess a cubic perovskite structure with the lattice space group Fm-3m generally represented by the group No. 225. The band structure of these compounds confirms their insulating nature. The calculated values of elastic parameters determined the brittle nature of Ba2ScSbO6 and Ba2YSbO6 compounds. Positive frequencies of the phonon dispersion curve indicates that these double perovskites are dynamically stable, with one acoustic and ten optical phonon modes having the combination of Raman active, Infrared active and optically inactive modes. The transport properties of these materials including electrical and thermal conductivity, as well as their thermoelectric power have been investigated. Additionally, the figure of merit was calculated to assess the suitability of double perovskites for thermoelectric devices and advanced technological applications.