26 pages, 14 figures.We study the possibility of identifying dark matter properties from XENON-like 100 kg experiments and the GLAST satellite mission. We show that whereas direct detection experiments will probe efficiently light WIMPs, given a positive detection (at the 10% level for $m_{\chi} \lesssim 50$ GeV), GLAST will be able to confirm and even increase the precision in the case of a NFW profile, for a WIMP-nucleon cross-section $\sigma_{\chi-p} \lesssim 10^{-8}$ pb. We also predict the rate of production of a WIMP in the next generation of colliders (ILC), and compare their sensitivity to the WIMP mass with the XENON and GLAST projects.The authors would like to thank the ENTApP Network of the ILIAS project RII3-CT-2004-506222 and he French ANR project PHYS@COL&COS for financial support. Y.M. would like to thank financial support via the "Marie Curie Host Fellowship for Transfer of Knowledge", MTKD-CT-2005-029466. The work of A. G. is sponsored by the hepTOOLS Research Training Network MRTN-CT-2006-035505. The work of C. M. was supported in part by the Spanish DGI of the MEC under Proyectos Nacionales FPA2006-01105 and FPA2006-05423, by the European Union under the RTN programs MRTN-CT-2004-503369 and UniverseNet MRTN-CT-2006-035863, and by the Comunidad de Madrid under Proyecto HEPHACOS S-0505/ESP-0346.Peer reviewed