We present the deepest Spitzer/InfraRed Array Camera (IRAC) 3.6, 4.5, 5.8, and 8.0 mu m wide-area mosaics yet over the Great Observatories Origins Deep Survey (GOODS)-N and GOODS-S fields as part of the GOODS Reionization Era wide-Area Treasury from Spitzer (GREATS) project. We reduced and mosaicked in a self-consistent way observations taken by the 11 different Spitzer/IRAC programs over the two GOODS fields from 12 yr of Spitzer cryogenic and warm-mission data. The cumulative depth in the 3.6 mu m and 4.5 mu m bands amounts to similar to 4260 hr, similar to 1220 hr of which are new very deep observations from the GREATS program itself. In the deepest area, the full-depth mosaics reach greater than or similar to 200 hr over an area of similar to 100 arcmin(2), corresponding to a sensitivity of similar to 29 AB magnitude at 3.6 mu m (1 sigma for point sources). Archival cryogenic 5.8 mu m and 8.0 mu m band data (a cumulative 976 hr) are also included in the release. The mosaics are projected onto the tangential plane of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey/GOODS at a 0.'' 3 pixel(-1) scale. This paper describes the methodology enabling, and the characteristics of, the public release of the mosaic science images, the corresponding coverage maps in the four IRAC bands, and the empirical point-spread functions (PSFs). These PSFs enable mitigation of the source blending effects by taking into account the complex position-dependent variation in the IRAC images. The GREATS data products are in the Infrared Science Archive. We also release the deblended 3.6-8.0 mu m photometry 9192 Lyman-break galaxies at z similar to 3.5-10. GREATS will be the deepest mid-infrared imaging until the James Webb Space Telescope and, as such, constitutes a major resource for characterizing early galaxy assembly.