We present the HIPASS Bright Galaxy Catalog (BGC), which contains the 1000 H I brightest galaxies in the southern sky as obtained from the H I Parkes All-Sky Survey (HIPASS). The selection of the brightest sources is based on their H I peak flux density (Speak gtrsim 116 mJy) as measured from the spatially integrated HIPASS spectrum. The derived H I masses range from ~107 to 4 × 1010 Modot. While the BGC (z <0.03) is complete in Speak, only a subset of ~500 sources can be considered complete in integrated H I flux density (F gtrsim 25 Jy km s-1). The HIPASS BGC contains a total of 158 new redshifts. These belong to 91 new sources for which no optical or infrared counterparts have previously been cataloged, an additional 51 galaxies for which no redshifts were previously known, and 16 galaxies for which the cataloged optical velocities disagree. Of the 91 newly cataloged BGC sources, only four are definite H I clouds: while three are likely Magellanic debris with velocities around 400 km s-1, one is a tidal cloud associated with the NGC 2442 galaxy group. The remaining 87 new BGC sources, the majority of which lie in the zone of avoidance, appear to be galaxies. We identified optical counterparts to all but one of the 30 new galaxies at Galactic latitudes |b| > 10°. Therefore, the BGC yields no evidence for a population of "free-floating" intergalactic H I clouds without associated optical counterparts. HIPASS provides a clear view of the local large-scale structure. The dominant features in the sky distribution of the BGC are the Supergalactic Plane and the Local Void. In addition, one can clearly see the Centaurus Wall, which connects via the Hydra and Antlia Clusters to the Puppis Filament. Some previously hardly noticable galaxy groups stand out quite distinctly in the H I sky distribution. Several new structures, including some not behind the Milky Way, are seen for the first time.