ZnO thin films co-doped with Mg and Ga (MxGyZzO, x + y + z = 1, x = 0.05, y = 0.02 and z = 0.93) were prepared on glass substrates by RF magnetron sputtering with different sputtering powers ranging from 100W to 200W at a substrate temperature of $350^{circ}C$. The effects of the sputtering power on the structural, morphological, electrical, and optical properties of MGZO thin films were investigated. The X-ray diffraction patterns showed that all the MGZO thin films were grown as a hexagonal wurtzite phase with the preferred orientation on the c-axis without secondary phases such as MgO, $Ga_2O_3$, or $ZnGa_2O_4$. The intensity of the diffraction peak from the (0002) plane of the MGZO thin films was enhanced as the sputtering power increased. The (0002) peak positions of the MGZO thin films was shifted toward, a high diffraction angle as the sputtering power increased. Cross-sectional field emission scanning electron microscopy images of the MGZO thin films showed that all of these films had a columnar structure and their thickness increased with an increase in the sputtering power. MGZO thin film deposited at the sputtering power of 200W showed the best electrical characteristics in terms of the carrier concentration ($4.71{ imes}10^{20}cm^{-3}$), charge carrier mobility ($10.2cm^2V^{-1}s^{-1}$) and a minimum resistivity ($1.3{ imes}10^{-3}{Omega}cm$). A UV-visible spectroscopy assessment showed that the MGZO thin films had high transmittance of more than 80 % in the visible region and that the absorption edges of MGZO thin films were very sharp and shifted toward the higher wavelength side, from 270 nm to 340 nm, with an increase in the sputtering power. The band-gap energy of MGZO thin films was widened from 3.74 eV to 3.92 eV with the change in the sputtering power.