Studies of the properties of low-redshift cluster galaxies suffer, in general, from small spatial coverage of the cluster area. WINGS, the most homogeneous and complete study of galaxies in dense environments to date, obtained spectroscopic redshifts for 48 clusters at a median redshift of 0.05, out to an average distance of approximately 0.5 cluster virial radii. The WINGS photometric survey was recently extended by the VST survey OmegaWINGS to cover the outskirts of a subset of the original cluster sample. In this work, we present the spectroscopic follow-up of 33 of the 46 clusters of galaxies observed with VST over 1 square degree. The aim of this spectroscopic survey is to enlarge the number of cluster members and study the galaxy characteristics and the cluster dynamical properties out to large radii, reaching the virial radius and beyond. We used the AAOmega spectrograph at AAT to obtain fiber-integrated spectra covering the wavelength region between 3800 and 9000 A, with a spectral resolution of 3.5-6 A full width at half maximum (FWHM). Observations were performed using two different configurations and exposure times per cluster. We measured redshifts using both absorption and emission lines and used them to derive the cluster redshifts and velocity dispersions. We present here the redshift measurements for 17985 galaxies, 7497 of which turned out to be cluster members. The sample magnitude completeness is 80% at V=20. Thanks to the observing strategy, the radial completeness turned out to be relatively constant (90%) within the AAOmega field of view. The success rate in measuring redshifts is 95%, at all radii. We provide redshifts for the full sample of galaxies in OmegaWINGS clusters together with updated and robust cluster redshift and velocity dispersions. These data will be publicly accessible through the CDS and VO archives.
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