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We present high-resolution maps of the dust reddening in the Magellanic Clouds (MCs). The maps cover the Large and Small Magellanic Cloud (LMC and SMC) area and have a spatial angular resolution between $\sim$ 26 arcsec and 55 arcmin. Based on the data from the optical and near-infrared (IR) photometric surveys, including the Gaia Survey, the SkyMapper Southern Survey (SMSS), the Survey of the Magellanic Stellar History (SMASH), the Two Micron All Sky Survey (2MASS) and the near-infrared $YJK_{\rm{S}}$ VISTA survey of the Magellanic Clouds system (VMC), we have obtained multi-band photometric stellar samples containing over 6 million stars in the LMC and SMC area. Based on the measurements of the proper motions and parallaxes of the individual stars from Gaia Early Data Release 3 (Gaia EDR3), we have built clean samples that contain stars from the LMC, SMC and Milky Way (MW), respectively. We apply the spectral energy distribution (SED) fitting to the individual sample stars to estimate their reddening values. As a result, we have derived the best-fitting reddening values of ~ 1.9 million stars in the LMC, 1.5 million stars in the SMC and 0.6 million stars in the MW, which are used to construct dust reddening maps in the MCs. Our maps are consistent with those from the literature. The resultant high-resolution dust maps in the MCs are not only important tools for reddening correction of sources in the MCs, but also fundamental for the studies of the distribution and properties of dust in the two galaxies.