We present optical spectroscopy for an X-ray and optical flux-limited sample of 677 XMM-Newton selected targets covering the 2 deg^2 COSMOS field, with a yield of 485 high-confidence redshifts. The majority of the spectra were obtained over three seasons (2005-2007) with the IMACS instrument on the Magellan (Baade) telescope. We also include in the sample previously published Sloan Digital Sky Survey spectra and supplemental observations with MMT/Hectospec. We detail the observations and classification analyses. The survey is 90% complete to flux limits of f_{0.5-10 keV}>8 x 10^-16 erg cm^-2 s^-1 and i_AB+<22, where over 90% of targets have high-confidence redshifts. Making simple corrections for incompleteness due to redshift and spectral type allows for a description of the complete population to $i_AB+<23. The corrected sample includes 57% broad emission line (Type 1, unobscured) AGN at 0.13<z<4.26, 25% narrow emission line (Type 2, obscured) AGN at 0.07<z<1.29, and 18% absorption line (host-dominated, obscured) AGN at 0<z<1.22 (excluding the stars that made up 4% of the X-ray targets). We show that the surveys limits in X-ray and optical flux include nearly all X-ray AGN (defined by L_{0.5-10 keV}>3 x 10^42 erg s^-1) to z<1, of both optically obscured and unobscured types. We find statistically significant evidence that the obscured to unobscured AGN ratio at z<1 increases with redshift and decreases with luminosity.
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