We present the first low-frequency Murchison Widefield Array (MWA) radio continuum maps of the Magellanic Clouds (MCs), usingmosaics from the GaLactic Extragalactic All-SkyMWA (GLEAM) survey. In this paper, we discuss the overall radio continuum morphology between 76 and 227 MHz and compare them with neutral hydrogen maps, 1.4 GHz continuum maps and optical images. Variation of diffuse emission is noticeable across the Large Magellanic Cloud (LMC) but absent across the bar of the Small Magellanic Cloud (SMC). We also measure the integrated flux densities and derive the spectral indices for the MCs. A double power-law model with fixed α1 = -0.1 fit between 19.7 MHz and 8.55 GHz yields α0 = -0.66 ± 0.08 for the LMC. A power-law model yields α8.55GHz 85.5MHz = -0.82 ± 0.03 for the SMC. The radio spectral index maps reveal distinctive flat and steep spectral indices for the HII regions and supernova remnants, respectively. We find strong correlation between HII regions and Ha emission. Using a new 150 MHz-Hα relation as a star formation rate indicator, we estimate global star formation rates of 0.068-0.161 M⊙ yr-1 and 0.021-0.050 M⊙ yr-1 for the LMC and SMC, respectively. Images in 20 frequency bands, and wideband averages are made available via the GLEAM virtual observatory server.