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We present maps of the Large and Small Magellanic Clouds from combined South Pole Telescope (SPT) and Planck data. The Planck satellite observes in nine bands, while the SPT data used in this work were taken with the three-band SPT-SZ camera, The SPT-SZ bands correspond closely to three of the nine Planck bands, namely those centered at 1.4, 2.1, and 3.0 mm. The angular resolution of the Planck data ranges from 5 to 10 arcmin, while the SPT resolution ranges from 1.0 to 1.7 arcmin. The combined maps take advantage of the high resolution of the SPT data and the long-timescale stability of the space-based Planck observations to deliver robust brightness measurements on scales from the size of the maps down to ∼1 arcmin. In each band, we first calibrate and color-correct the SPT data to match the Planck data, then we use noise estimates from each instrument and knowledge of each instrument's beam to make the inverse-variance-weighted combination of the two instruments' data as a function of angular scale. We create maps assuming a range of underlying emission spectra and at a range of final resolutions. We perform several consistency tests on the combined maps and estimate the expected noise in measurements of features in them. We compare maps from this work to those from the Herschel HERITAGE survey, finding general consistency between the data sets. All data products described in this paper are available for download from the NASA Legacy Archive for Microwave Background Data Analysis server.