Massive stars briefly pass through the yellow supergiant (YSG) phase as they evolve redward across the H-R diagram and expand into red supergiants (RSGs). Higher-mass stars pass through the YSG phase again as they evolve blueward after experiencing significant RSG mass loss. These post-RSG objects offer us a tantalizing glimpse into which stars end their lives as RSGs and why. One telltale sign of a post-RSG object may be an instability to pulsations, depending on the star's interior structure. Here we report the discovery of five YSGs with pulsation periods faster than 1 day, found in a sample of 76 cool supergiants observed by the Transiting Exoplanet Survey Satellite (TESS) at a two-minute cadence. These pulsating YSGs are concentrated in an H-R diagram region not previously associated with pulsations; we conclude that this is a genuine new class of pulsating star, fast yellow pulsating supergiants (FYPSs). For each FYPS, we extract frequencies via iterative prewhitening and conduct a time-frequency analysis. One FYPS has an extracted frequency that is split into a triplet, and the amplitude of that peak is modulated on the same timescale as the frequency spacing of the triplet; neither rotation nor binary effects are likely culprits. We discuss the evolutionary status of FYPS and conclude that they are candidate post-RSGs. All stars in our sample also show the same stochastic low-frequency variability found in hot OB stars and attributed to internal gravity waves. Finally, we find four {alpha} Cygni variables in our sample, of which three are newly discovered.