Nuclear obscuration plays a key role in the initial phases of AGN growth, yet not many highly obscured AGN are currently known beyond the local Universe, and their search is an active topic of research. The XMM-Newton survey in the Chandra Deep Field South (XMM-CDFS) aims at detecting and studying the spectral properties of a significant number of obscured and Compton-thick (NH=10^24^cm^-2^ ) AGN. The large effective area of XMM-Newton in the 2-10 and 5-10keV bands, coupled with a 3.45Ms nominal exposure time (2.82 and 2.45Ms after lightcurve cleaning for MOS and PN respectively), allows us to build clean samples in both bands, and makes the XMM-CDFS the deepest XMM-Newton survey currently published in the 5-10keV band. The large multi- wavelength and spectroscopic coverage of the CDFS area allows for an immediate and abundant scientific return. In this paper, we present the data reduction of the XMM-CDFS observations, the method for source detection in the 2-10 and 5-10keV bands, and the resulting catalogues. A number of 339 and 137 sources are listed in the above bands with flux limits of 6.6x10^-16^ and 9.5x10^-16^erg/s/cm^2^, respectively. The flux limits at 50% of the maximum sky coverage are 1.8x10^-15^ and 4.0x10^-15^erg/s/cm^2^, respectively. The catalogues have been cross-correlated with the Chandra ones: 315 and 130 identifications have been found with a likelihood- ratio method, respectively. A number of 15 new sources, previously undetected by Chandra, is found; 5 of them lie in the 4Ms area. Redshifts, either spectroscopic or photometric, are available for ~92% of the sources. The number counts in both bands are presented and compared to other works. The survey coverage has been calculated with the help of two extensive sets of simulations, one set per band. The simulations have been produced with a newly-developed simulator, written with the aim of the most careful reproduction of the background spatial properties. For this reason, we present a detailed decomposition of the XMM-Newton background into its components: cosmic, particle, and residual soft protons. The three components have different spatial distributions. The importance of these three components depends on the band and on the camera; the particle background is the most important one (80-90% of the background counts), followed by the soft protons (4-20%).