Context: ω Centauri is the most well studied Galactic Globular Cluster because of its numerous puzzling features: significant dispersion in metallicity, multiple populations, triple main-sequence, horizontal branch morphology, He-rich population(s), and extended star-formation history. Intensive spectroscopic follow-up observing campaigns targeting stars at different positions in the color-magnitude diagram promises to clarify some of these peculiarities. Aims: To be able to target cluster members reliably during spectroscopic surveys and both spatial and radial distributions in the cluster outskirts without including field stars, a high quality proper-motion catalog of ω Cen and membership probability determination are required. The only available wide field proper-motion catalog of ω Cen is derived from photographic plates, and only for stars brighter than B~16. Using ESO archive data, we create a new, CCD-based, proper-motion catalog for this cluster, extending to B~20. Methods: We used high precision astrometric software developed specifically for data acquired by WFI@2.2m telescope and presented in the first paper of this series. We demonstrated previously that a 7 mas astrometric precision level can be achieved with this telescope and camera for well exposed stars in a single exposure, assuming an empirical PSF and a local transformation approach in measuring star displacements. Results: We achieved a good cluster-field separation with a temporal base-line of only four years. We corrected our photometry for sky-concentration effects. We provide calibrated photometry for UBVR_CIC wide-band data plus narrow-band filter data centered on Hα for almost 360 000 stars. We confirm that the ω Cen metal-poor and metal-rich components have the same proper motion, and demonstrate that the metal-intermediate component in addition exhibits the same mean motion as the other RGB stars. We provide membership probability determinations for published ω Cen variable star catalogs. Conclusions: Our catalog extends the proper-motion measurements to fainter than the cluster turn-off luminosity, and covers a wide area (˜33 arcmin×33 arcmin) around the center of ω Cen. Our catalog is electronically available to the astronomical community. Based on archive observations with the MPI/ESO 2.2 m telescope, located at La Silla and Paranal Observatory, Chile. Table 6 (catalog) is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/493/959