(Abridged) We present the results of the systematic survey of X-ray sources in the central region of M31 using the data from XMM-Newton observations performed in the years 2000-2004. The spectral properties and variability of 123 bright X-ray sources with apparent luminosities between ~10^{36} and ~5x10^{38} ergs/s were studied in detail. The spectral distribution of M31 X-ray sources, based on the spectral fitting with a power law model is clearly bimodal with a main peak corresponding to a photon index Gamma ~ 1.75 and a shoulder at Gamma ~ 2.0-2.2 extending to the soft spectral region, and shows clear evolution with source luminosity. The distribution of absorbing columns towards M31 sources derived from spectral analysis has a peak at N_H~1.2x10^{21} cm^{-2} extending up to 1.3x10^{22} cm^{-2}, with an average value of (1.52 +/- 0.02)x10^{21} cm^{-2}. More than 80% of sources observed in two or more observations show significant variability on the time scales of days to years. About 50% of the sources in our sample are spectrally variable. The spectral evolution of a number of sources is correlated with the level of their X-ray flux, while some sources demonstrate complex patterns of evolution on the hardness-intensity diagram. Based on the similarity of the properties of M31 X-ray sources and their Galactic counterparts, we expect most of the X-ray sources in our sample to be accreting binary systems with neutron star and black hole primaries. A total of 44 X-ray sources can be identified as probable X-ray binaries. Combining the results of X-ray analysis with available data at other wavelengths, we classify 7% and 24% of sources in our sample as, respectively, probable black hole and neutron star candidates.
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