We report the final optical identifications of the medium-depth ({approx}60 ks), contiguous (2 deg{sup 2}) XMM-Newton survey of the COSMOS field. XMM-Newton has detected {approx}1800 X-ray sources down to limiting fluxes of {approx}5 x 10{sup -16}, {approx}3 x 10{sup -15}, and {approx}7 x 10{sup -15} erg cm{sup -2} s{sup -1} in the 0.5-2 keV, 2-10 keV, and 5-10 keV bands, respectively ({approx}1 x 10{sup -15}, {approx}6 x 10{sup -15}, and {approx}1 x 10{sup -14} erg cm{sup -2} s{sup -1}, in the three bands, respectively, over 50% of the area). The work is complemented by an extensive collection of multiwavelength data from 24 {mu}m to UV, available from the COSMOS survey, for each of the X-ray sources, including spectroscopic redshifts for {approx}>50% of the sample, and high-quality photometric redshifts for the rest. The XMM and multiwavelength flux limits are well matched: 1760 (98%) of the X-ray sources have optical counterparts, 1711 ({approx}95%) have IRAC counterparts, and 1394 ({approx}78%) have MIPS 24 {mu}m detections. Thanks to the redshift completeness (almost 100%) we were able to constrain the high-luminosity tail of the X-ray luminosity function confirming that the peak of the number density of log L{sub X} > 44.5 active galactic nuclei (AGNs) is at z {approx} 2. Spectroscopically identified obscured and unobscured AGNs, as well as normal and star-forming galaxies, present well-defined optical and infrared properties. We devised a robust method to identify a sample of {approx}150 high-redshift (z > 1), obscured AGN candidates for which optical spectroscopy is not available. We were able to determine that the fraction of the obscured AGN population at the highest (L{sub X} > 10{sup 44} erg s{sup -1}) X-ray luminosity is {approx}15%-30% when selection effects are taken into account, providing an important observational constraint for X-ray background synthesis. We studied in detail the optical spectrum and the overall spectral energy distribution of a prototypical Type 2 QSO, caught in a stage transitioning from being starburst dominated to AGN dominated, which was possible to isolate only thanks to the combination of X-ray and infrared observations.