Heavily obscured, Compton Thick (CT, NH>10^24 cm^-2) AGN may represent an important phase in AGN/galaxy co-evolution and are expected to provide a significant contribution to the cosmic X-ray background (CXB). Through direct X-ray spectra analysis, we selected 39 heavily obscured AGN (NH>3x10^23 cm^-2) in the 2 deg^2 XMM-COSMOS survey. After selecting CT AGN based on the fit of a simple absorbed two power law model to the XMM data, the presence of CT AGN was confirmed in 80% of the sources using deeper Chandra data and more complex models. The final sample of CT AGN comprises 10 sources spanning a large range of redshift and luminosity. We collected the multi-wavelength information available for all these sources, in order to study the distribution of SMBH and host properties, such as BH mass (M_BH), Eddington ratio (λ_Edd), stellar mass (M*), specific star formation rate (sSFR) in comparison with a sample of unobscured AGN. We find that highly obscured sources tend to have significantly smaller M_BH and higher λ_edd with respect to unobscured ones, while a weaker evolution in M* is observed. The sSFR of highly obscured sources is consistent with the one observed in the main sequence of star forming galaxies, at all redshift. We also present optical spectra, spectral energy distribution (SED) and morphology for the sample of 10 CT AGN: all the available optical spectra are dominated by the stellar component of the host galaxy, and a highly obscured torus component is needed in the SED of the CT sources. Exploiting the high resolution Hubble-ACS images available, we conclude that these highly obscured sources have a significantly larger merger fraction with respect to other X-ray selected samples of AGN. Finally we discuss implications in the context of AGN/galaxy co-evolutionary models, and compare our results with the predictions of CXB synthesis models. ; Comment: Revised version after referee comments. Accepted for publication in Astronomy & Astrophysics on 25 November 2014. 23 pages, 2 tables, 16 figures