We present a catalog of optical spectroscopic identifications of sources detected by Spitzer at 3.6 or 24 micron down to 10 and 280 microJy, respectively, in the SWIRE/XMM-Newton/ELAIS-S1 field and classified via line width analysis and diagnostic diagrams. A total of 1376 sources down to R~24.2 mag have been identified (1362 detected at 3.6 micron, 419 at 24 micron, and 405 at both) by low-resolution optical spectroscopy carried out with FORS2, VIMOS, and EFOSC2 at the Very Large Telescope and 3.6m ESO telescopes. The spectroscopic campaigns have been carried out over the central 0.6 square degrees area of ELAIS-S1 which, in particular, has also been observed by XMM-Newton and Chandra. We find the first direct optical spectroscopic evidence that the fraction of active galactic nuclei (AGN; mostly AGN2) increases with increasing F(24 micron)/F(R) ratio, reaching values of 70(+/-20)% in the range 316<F(24 micron)F(R)<1000. We present an IRAC-MIPS color-color diagram able to separate AGN1 from obscured AGN2 candidates. After having corrected for the spectroscopic incompleteness of our sample, it results that the AGN fraction at F(24 micron)=0.8 mJy is ~22(+/-7)% and decreases slowly to ~19(+/-5)% down to F(24 micron)=0.3 mJy.