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MIGHTEE is a galaxy evolution survey using simultaneous radio continuum,spectro-polarimetry, and spectral line observations from the South AfricanMeerKAT telescope. When complete, the survey will image $\sim$20 deg$^{2}$ overthe COSMOS, E-CDFS, ELAIS-S1, and XMM-LSS extragalactic deep fields with acentral frequency of 1284 MHz. These were selected based on the extensivemultiwavelength datasets from numerous existing and forthcoming observationalcampaigns. Here we describe and validate the data processing strategy for thetotal intensity continuum aspect of MIGHTEE, using a single deep pointing inCOSMOS (1.6 deg$^{2}$) and a three-pointing mosaic in XMM-LSS (3.5 deg$^{2}$).The processing includes the correction of direction-dependent effects, andresults in thermal noise levels below 2~$\mathrm{\mu}$Jy beam$^{-1}$ in bothfields, limited in the central regions by classical confusion at $\sim$8$''$angular resolution, and meeting the survey specifications. We also produceimages at $\sim$5$''$ resolution that are $\sim$3 times shallower. Theresulting image products form the basis of the Early Science continuum datarelease for MIGHTEE. From these images we extract catalogues containing 9,896and 20,274 radio components in COSMOS and XMM-LSS respectively. We also processa close-packed mosaic of 14 additional pointings in COSMOS and use these inconjunction with the Early Science pointing to investigate methods for primarybeam correction of broadband radio images, an analysis that is of relevance toall full-band MeerKAT continuum observations, and wide field interferometricimaging in general. A public release of the MIGHTEE Early Science continuumdata products accompanies this article.

MIGHTEE: total intensity radio continuum imaging and the COSMOS / XMM-LSS Early Science fields