Context. The Frontier Fields survey is a pioneering observational program aimed at collecting photometric data, both from space (Hubble Space Telescope and Spitzer Space Telescope) and from ground-based facilities (VLT Hawk-I), for six deep fields pointing at clusters of galaxies and six nearby deep parallel fields, in a wide range of passbands. The analysis of these data is a natural outcome of the Astrodeep project, an EU collaboration aimed at developing methods and tools for extragalactic photometry and creating valuable public photometric catalogues. Aims. We produce multiwavelength photometric catalogues (from B to 4.5 µm) for the first two of the Frontier Fields, Abell-2744 and MACS-J0416 (plus their parallel fields). Methods. 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, and the intra-cluster light. We perform the detection on the processed HST H160 image to obtain a pure H-selected sample, which is the primary catalogue that we publish. We also add a sample of sources which are undetected in the H160 image but appear on a stacked infrared image. Photometry on the other HST bands is obtained using SExtractor, again on processed images after the procedure for foreground light removal. Photometry on the Hawk-I and IRAC bands is 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.Results. The procedure of foreground light subtraction 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 the 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 µm from Spitzer. full and detailed treatment of photometric errors is included. We perform basic sanity checks on the reliability of our results. Conclusions. The multiwavelength photometric catalogues are available publicly and are ready to be used for scientific purposes. Our procedures allows for the detection of outshone 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 Paper II.