First principle calculations are performed to investigate the electronic structure, structural phase stability, optical properties and thermoelectric properties of double perovskite oxide semiconductors namely Sr2AlM'O6 (M' = Nb and Ta) in the cubic symmetry using WIEN2k. In order to study the ground state properties of these compounds, the total energies are calculated as a function of reduced volumes and fitted with Brich Murnaghan equation. The estimated ground state parameters are comparable with the available experimental data. Calculations of electronic band structure on these compounds have been carried out using generalized gradient approximations and modified Becke-Johanson potential (TB-mBJ). The calculated band gap for Sr2AlNbO6 and Sr2AlTaO6 with GGA and TB-mBJ reveal that these compounds exhibit semiconducting behavior with a direct band gap. To explore the optical transitions in these compounds, the real and imaginary parts of the dielectric function, refractive index, extinction coefficient, reflectivity, optical absorption coefficient, real part of optical conductivity and the energy-loss function are calculated at ambient conditions and analyzed both with GGA and TB-mBJ potentials. Investigations of the thermoelectric properties of these compounds have been carried out by the calculations of transport coefficients based on Boltzmann transport theory in order to analyze the variation of Seebeck's coefficient at different temperatures for various carrier concentrations based on the electronic structure near the valence band maxima.