A method for preparation of dense Y2O3–MgO composite ceramics by the microwave sintering was developed. The initial powders were obtained by glycine-nitrate self-propagating high-temperature synthesis (SHS) with different oxidant-to-fuel ratio. Density and IR-transmission of microwave sintered Y2O3–MgO ceramics increase with respect to dispersity of the SHS-powders and reach its maximum values for the powder prepared in a 20% fuel excess. The sintering behavior of Y2O3–MgO compacts was investigated by optical dilatometry and measuring an electric conductivity upon heating. Significant microwave radiation power surges at temperatures of 900–1000 °C, caused by the decomposition of magnesium carbonate, have been found. As a result of matching the conditions for the synthesis of powders and sintering modes, a transmission of composite ceramics of 78% at a wavelength of 6 μm was achieved at a maximum processing temperature of 1500 °C.