The IRAC ultradeep field (IUDF) and IRAC Legacy over GOODS (IGOODS) programs are two ultradeep imaging surveys at 3.6{mu}m and 4.5{mu}m with the Spitzer Infrared Array Camera (IRAC). The primary aim is to directly detect the infrared light of reionization epoch galaxies at z > 7 and to constrain their stellar populations. The observations cover the Hubble Ultra Deep Field (HUDF), including the two HUDF parallel fields, and the CANDELS/GOODS-South, and are combined with archival data from all previous deep programs into one ultradeep dataset. The resulting imaging reaches unprecedented coverage in IRAC 3.6{mu}m and 4.5{mu}m ranging from > 50 hour over 150 arcmin^2, > 100 hour over 60 sq arcmin2, to 200 hour over 5 - 10 arcmin$^2$. This paper presents the survey description, data reduction, and public release of reduced mosaics on the same astrometric system as the CANDELS/GOODS-South WFC3 data. To facilitate prior-based WFC3+IRAC photometry, we introduce a new method to create high signal-to-noise PSFs from the IRAC data and reconstruct the complex spatial variation due to survey geometry. The PSF maps are included in the release, as are registered maps of subsets of the data to enable reliability and variability studies. Simulations show that the noise in the ultradeep IRAC images decreases approximately as the square root of integration time over the range 20 - 200 hours, well below the classical confusion limit, reaching 1{sigma} point source sensitivities as faint as of 15 nJy (28.5 AB) at 3.6{mu}m and 18 nJy (28.3 AB) at 4.5{mu}m. The value of such ultradeep IRAC data is illustrated by direct detections of z = 7 - 8 galaxies as faint as HAB = 28.
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