The structural, elastic, mechanical, magneto-electronic, and thermoelectric properties of Sr2TiCoO6 double perovskite oxide have been studied within the framework of density functional theory. The FP-LAPW method within the (GGA) and (mBJ) approximations is chosen in the computational approach. This alloy crystallizes in cubic structure with the ferromagnetic phase. The computed lattice constant was found to agree with the available experimental results. This compound shows the half-metallic ferromagnetic properties. A value of 1 µB is found for the total magnetic moment with an important contribution from Co atoms. The elastic parameters reveal that Sr2TiCoO6 as being super hard and brittle. We calculated the thermoelectric properties of Sr2TiCoO6 using the Boltzmann transport equations within the DFT in a temperature range from 100 to 1000 K. The transport parameters like Seebeck coefficient, electrical thermal conductivity and the merit factor, have been put together to establish their thermoelectric response. The figure of merit value is between [0.71-0.99] indicating that our compound is a good candidate for thermoelectric applications at high and low temperatures.