This is the second paper of a series describing the Asiago-ESO/RASS QSO survey, a project aimed at the construction of an all-sky, statistically well defined sample of very bright QSOs (BJ<=15). Such a survey is required to remove the present uncertainties about the properties of the local QSO population and constitutes an homogeneous database for detailed evolutionary studies of active galactic nuclei (AGNs). We present here the complete southern sample, which comprises 243 bright (12.60<=BJ<=15.13) QSO candidates at high galactic latitudes (|b_gal_|>=30{deg}). The area covered by the survey is 5660deg^2^. Spectroscopy for the 137 still unidentified objects has been obtained. The total number of AGNs turns out to be 11163 of which are new identifications. The properties of the selection are discussed. The completeness and the success rate for this survey at the final stage are 63% and 46%, respectively.