We study the spatial clustering of 538 X-ray selected AGN in the 2 deg^2 XMM-COSMOS field that are spectroscopically identified to I_{AB}<23 and span the redshift range z=0.2-3.0. The median redshift and luminosity of the sample are z = 0.98 and L_{0.5-10}=6.3 x 10^{43} erg/s, respectively. A strong clustering signal is detected at ~18sigma level, which is the most significant measurement obtained to date for clustering of X-ray selected AGN. By fitting the projected correlation function w(r_p) with a power law on scales of r_p=0.3-40 Mpc/h, we derive a best fit comoving correlation length of r_0 = 8.6 +- 0.5 Mpc/h and slope of gamma=1.88 +- 0.07 (Poissonian errors; bootstrap errors are about a factor of 2 larger). An excess signal is observed in the range r_p~5-15 Mpc/h, which is due to a large scale structure at z ~ 0.36 containing about 40 AGN. When removing the z ~ 0.36 structure, or computing w(r_p) in a narrower range around the peak of the redshift distribution (e.g. z=0.4-1.6), the correlation length decreases to r_0 ~ 5-6 Mpc/h, which is consistent with that observed for bright optical QSOs at the same redshift. We investigate the clustering properties of obscured and unobscured AGN separately. Within the statistical uncertainties, we do not find evidence that AGN with broad optical lines (BLAGN) cluster differently from AGN without broad optical lines (non-BLAGN). The correlation length measured for XMM-COSMOS AGN at z~1 is similar to that of massive galaxies (stellar mass M_*> 3 x 10^{10} M_sun) at the same redshift. This suggests that AGN at z~1 are preferentially hosted by massive galaxies, as observed both in the local and in the distant (z~2) Universe. (shortened) Comment: 16 pages, 11 figures; accepted for publication in A&A. Language edited version