In this paper we introduce the deepest and most extensive ultraviolet extragalactic source catalogs of the Virgo Cluster area to date. Archival and targeted GALEX imaging is compiled and combined to provide the deepest possible coverage over ~120deg^2^ in the NUV (lambda_eff_=2316{AA}) and ~40deg^2^ in the FUV (lambda_eff_=1539{AA}) between 180{deg}<=RA<=195{deg} and 0{deg}<=DE<=20{deg}. We measure the integrated photometry of 1770 extended UV sources of all galaxy types and use GALEX pipeline photometry for 1,230,855 point-like sources in the foreground, within, and behind the cluster. Extended source magnitudes are reliable to m_UV_~22, showing a ~0.01{sigma} difference from their asymptotic magnitudes. Point-like source magnitudes have a 1{sigma} standard deviation within ~0.2mag down to m_uv_~23. The point-like source catalog is cross-matched with large optical databases and surveys including the SDSS DR9 (>1 million Virgo Cluster sources), the Next Generation Virgo Cluster Survey (NGVS; >13 million Virgo Cluster sources), and the NED (~30,000 sources in the Virgo Cluster). We find that 69% of the entire UV point-like source catalog has a unique optical counterpart, 11% of which are stars and 0.01% (129) are Virgo cluster members that are neither in the VCC nor part of the bright CGCG galaxy catalog (i.e., m_pg_<14.5). These data are collected in three catalogs containing the UV extended sources, the UV point-like sources, and the most relevant optical parameters of UV-optically matched point-like sources for further studies from SDSS. The GUViCS catalogs provide a unique set of data for future work on UV and multiwavelength studies in the cluster and background environments.