We report the definite spectroscopic identification of 41 OB supergiants, giants and main sequence stars in the central parsec of the Galaxy. Detection of their absorption lines have become possible with the high spatial and spectral resolution and sensitivity of the adaptive optics integral field spectrometer SPIFFI/SINFONI on the ESO VLT. Several of these OB stars appear to be helium and nitrogen rich. Almost all of the ~80 massive stars now known in the central parsec (central arcsecond excluded) reside in one of two somewhat thick (<|h|/R>~0.14) rotating disks. These stellar disks have fairly sharp inner edges (R~1) and surface density profiles that scale as R^{-2}. We do not detect any OB stars outside the central 0.5 pc. The majority of the stars in the clockwise system appear to be on almost circular orbits, whereas most of those in the `counter-clockwise disk appear to be on eccentric orbits. Based on its stellar surface density distribution and dynamics we propose that IRS 13E is an extremely dense cluster (core density > 3x10^8 sunmass/pc^3), which has formed in the counter-clockwise disk. The stellar contents of both systems are remarkably similar, indicating a common age of ~6+/-2 Myr. The K-band luminosity function of the massive stars suggests a top-heavy mass function and limits the total stellar mass contained in both disks to ~1.5x10^4 sunmass. Our data strongly favor in situ star formation from dense gas accretion disks for the two stellar disks. This conclusion is very clear for the clockwise disk and highly plausible for the counter-clockwise system.