Homogeneous abundances of light elements, alpha-elements, Fe-group elements and neutron-capture elements from high-resolution FLAMES spectra are presented for stars in the globular cluster NGC 5634, associated to the Sagittarius dwarf spheroidal galaxy. In particular we present detailed chemical abundance of 22 species for the seven stars observed with UVES-FLAMES, and the abundance of six elements for stars observed with GIRAFFE. We derived a metallicity [Fe/H]=-1.867+/-0.019+/-0.065dex (+/-statistical+/-systematic error) with sigma=0.050dex (7 stars). We found the normal anti-correlations between light elements (Na and O, Mg and Al), signature of multiple populations typical of massive and old GCs. We confirm the associations of NGC 5634 to the Sgr dSph, from which the cluster was lost a few Gyr ago, on the basis of its velocity and position, and the abundance ratios of {alpha} and neutron capture elements.