The aim of this paper is to introduce the WIRCam Ultra Deep Survey (WUDS), a near-IR photometric survey carried out at the CFH Telescope in the field of the CFHTLS-D3 field (Groth Strip). WUDS includes four near-IR bands (Y, J, H and Ks) over a field of view of ˜400 arcmin2. The typical depth of WUDS data reaches between ˜26.8 in Y and J, and ˜26 in H and Ks (AB, 3σ in 1.3″ aperture), whereas the corresponding depth of the CFHTLS-D3 images in this region ranges between 28.6 and 29 in ugr, 28.2 in i and 27.1 in z (same S/N and aperture). The area and depth of this survey were specifically tailored to set strong constraints on the cosmic star formation rate and the luminosity function brighter or around L⋆ in the z ˜ 6 - 10 redshift domain, although these data are also useful for a variety of extragalactic projects. This first paper is intended to present the properties of the public WUDS survey in details: catalog building, completeness and depth, number counts, photometric redshifts, and global properties of the galaxy population. We have also concentrated on the selection and characterization of galaxy samples at z ˜ [4.5 - 7] in this field. For these purposes, we include an adjacent shallower area of ˜1260 arcmin2 in this region, extracted from the WIRCam Deep Survey (WIRDS), and observed in J, H and Ks bands. UV luminosity functions were derived at z ˜ 5 and z ˜ 6 taking advantage from the fact that WUDS covers a particularly interesting regime at intermediate luminosities, which allows a combined determination of M⋆ and Φ⋆ with increased accuracy. Our results on the luminosity function are consistent with a small evolution of both M⋆ and Φ⋆ between z = 5 and z = 6, irrespective of the method used to derive them, either photometric redshifts applied to blindly-selected dropout samples or the classical Lyman Break Galaxy color-preselected samples. Our results lend support to higher Φ⋆ determinations at z = 6 than usually reported. The selection and combined analysis of different galaxy samples at z ≥ 7 will be presented in a forthcoming paper, as well as the evolution of the UV luminosity function between z ˜ 4.5 and 9. WUDS is intended to provide a robust database in the near-IR for the selection of targets for detailed spectroscopic studies, in particular for the EMIR/GTC GOYA Survey. A copy of the data products is also available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/620/A51