Omega Centauri is the most well studied Globular Cluster because of its numerous puzzling features. Intensive spectroscopic follow-up observing campaigns targeting stars at different positions on the color-magnitude diagram promises to clarify some of these peculiarities. To 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 omega Cen and membership probability determination are required. The only available wide field proper-motion catalog of omega 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. We used the high precision astrometric software developed specifically for data acquired by WFI@2.2m telescope and presented in the first paper of this series. 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 UBVRI wide-band data plus narrow-band filter data centered on H_alpha for almost 360 000 stars. We can confirm that the omega Cen metal-poor and the 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 provided membership probability determination for published omega Cen variable star catalogs. Our catalog extends the proper-motion measurements to fainter than the cluster turn-off luminosity, and covers a wide area (~33x33) around the center of omega Cen. Our catalog is now electronically available to the astronomical community.
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