The Kilodegree Extremely Little Telescope (KELT) project has been conducting a photometric survey of transiting planets orbiting bright stars for over 10 years. The KELT images have a pixel scale of ~23"/pixel very similar to that of NASA's Transiting Exoplanet Survey Satellite (TESS) - as well as a large point-spread function, and the KELT reduction pipeline uses a weighted photometric aperture with radius 3'. At this angular scale, multiple stars are typically blended in the photometric apertures. In order to identify false positives and confirm transiting exoplanets, we have assembled a follow-up network (KELT-FUN) to conduct imaging with spatial resolution, cadence, and photometric precision higher than the KELT telescopes, as well as spectroscopic observations of the candidate host stars. The KELT-FUN team has followed-up over 1600 planet candidates since 2011, resulting in more than 20 planet discoveries. Excluding ~450 false alarms of non-astrophysical origin (i.e., instrumental noise or systematics), we present an all-sky catalog of the 1128 bright stars (6<V<13) that show transit-like features in the KELT light curves, but which were subsequently determined to be astrophysical false positives (FPs) after photometric and/or spectroscopic follow-up observations. The KELT-FUN team continues to pursue KELT and other planet candidates and will eventually follow up certain classes of TESS candidates. The KELT FP catalog will help minimize the duplication of follow-up observations by current and future transit surveys such as TESS.