The IRAS Revised Bright Galaxy Sample (RBGS) is a complete flux-limited survey of extragalactic objects with total 60 μm flux density greater than 5.24 Jy, covering the entire sky surveyed by the Infrared Astronomical Satellite (IRAS) at Galactic latitude |b| > 5°. The RBGS includes 629 objects, with a median sample redshift of 0.0082 and a maximum redshift of 0.0876. It supersedes the previous IRAS Bright Galaxy Samples (BGS1+BGS2), which were compiled before the final ("Pass 3") calibration of the IRAS Level 1 Archive in May 1990. The RBGS uses more accurate and consistent automated methods to measure the flux of objects with extended emission. The RBGS contains 39 new objects not present in BGS1+BGS2, and 28 objects from BGS1+BGS2 have been dropped due to revised 60 μm flux densities below 5.24 Jy. The RBGS provides revised 12 μm, 25 μm, 60 μm, and 100 μm total flux densities for all 629 infrared sources, along with source size information and derived infrared luminosities. An atlas of images from the Digitized Sky Survey, annotated with IRAS position uncertainty ellipses and scale bars, is included to aid in visualizing the optical morphology of the sources. The revised bolometric infrared luminosity function for infrared bright galaxies in the local Universe is best fit by a double power law, φ(LIR) ∝ Lα, with α = −0.6 (±0.1) below and above the "characteristic" infrared luminosity LIR ∼ 1010.5 L⊙. A companion paper provides High Resolution (HIRES) processing of over 100 RBGS sources, improving spatial resolution and allowing for better source positions or deconvolution of close galaxy pairs.The IRAS Revised Bright Galaxy Sample (RBGS) is a complete flux-limited survey of extragalactic objects with total 60 μm flux density greater than 5.24 Jy, covering the entire sky surveyed by the Infrared Astronomical Satellite (IRAS) at Galactic latitude |b| > 5°. The RBGS includes 629 objects, with a median sample redshift of 0.0082 and a maximum redshift of 0.0876. It supersedes the previous IRAS Bright Galaxy Samples (BGS1+BGS2), which were compiled before the final ("Pass 3") calibration of the IRAS Level 1 Archive in May 1990. The RBGS uses more accurate and consistent automated methods to measure the flux of objects with extended emission. The RBGS contains 39 new objects not present in BGS1+BGS2, and 28 objects from BGS1+BGS2 have been dropped due to revised 60 μm flux densities below 5.24 Jy. The RBGS provides revised 12 μm, 25 μm, 60 μm, and 100 μm total flux densities for all 629 infrared sources, along with source size information and derived infrared luminosities. An atlas of images from the Digitized Sky Survey, annotated with IRAS position uncertainty ellipses and scale bars, is included to aid in visualizing the optical morphology of the sources. The revised bolometric infrared luminosity function for infrared bright galaxies in the local Universe is best fit by a double power law, φ(LIR) ∝ Lα, with α = −0.6 (±0.1) below and above the "characteristic" infrared luminosity LIR ∼ 1010.5 L⊙. A companion paper provides High Resolution (HIRES) processing of over 100 RBGS sources, improving spatial resolution and allowing for better source positions or deconvolution of close galaxy pairs.