We present multiwavelength photometric catalogues (HST, Spitzer and Hawk-I K band) for the first two of the Frontier Fields, Abell2744 and MACSJ0416 (plus their parallel fields). To detect faint sources even in the central regions of the clusters, we develop a robust and repeatable procedure that uses the public codes Galapagos and Galfit to model and remove most of the light contribution from both the brightest cluster members as well as the ICL. We perform the detection on the HST H160 processed image to obtain a pure H-selected sample. We also add a sample of sources which are undetected in the H160 image but appear on a stacked infrared image. Photometry in the other HST bands is obtained using SExtractor, performed again on residual images after the Galfit procedure for foreground light removal. Photometry on the Hawk-I and IRAC bands has been obtained using our PSF-matching deconfusion code T-PHOT. A similar procedure, but without the need for the foreground light removal, is adopted for the Parallel fields. The procedure allows for the detection and the photometric measurements of ~2500 sources per field. We deliver and release complete photometric H-detected catalogues, with the addition of a complementary sample of infrared-detected sources. All objects have multiwavelength coverage including B to H HST bands, plus K band from Hawk-I, and 3.6 - 4.5 {mu}m from Spitzer. Full and detailed treatment of photometric errors is included. We perform basic sanity checks on the reliability of our results. The multiwavelength catalogues are publicly available and are ready to be used for scientific purposes. Our procedures allows for the detection of outshined objects near the bright galaxies, which, coupled with the magnification effect of the clusters, can reveal extremely faint high redshift sources. Full analysis on photometric redshifts is presented in a companion Paper II. [abridged]
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