NASA's Transiting Exoplanet Survey Satellite (TESS) mission promises to improve our understanding of hot Jupiters by providing an all-sky, magnitude-limited sample of transiting hot Jupiters suitable for population studies. Assembling such a sample requires confirming hundreds of planet candidates with additional follow-up observations. Here we present 20 hot Jupiters that were detected using TESS data and confirmed to be planets through photometric, spectroscopic, and imaging observations coordinated by the TESS Follow-up Observing Program. These 20 planets have orbital periods shorter than 7 days and orbit relatively bright FGK stars (10.9 < G < 13.0). Most of the planets are comparable in mass to Jupiter, although there are four planets with masses less than that of Saturn. TOI-3976b, the longest-period planet in our sample (P = 6.6 days), may be on a moderately eccentric orbit (e = 0.18 ± 0.06), while observations of the other targets are consistent with them being on circular orbits. We measured the projected stellar obliquity of TOI-1937A b, a hot Jupiter on a 22.4 hr orbit with the Rossiter-McLaughlin effect, finding the planet's orbit to be well aligned with the stellar spin axis (∣λ∣ = 4.°0 ± 3.°5). We also investigated the possibility that TOI-1937 is a member of the NGC 2516 open cluster but ultimately found the evidence for cluster membership to be ambiguous. These objects are part of a larger effort to build a complete sample of hot Jupiters to be used for future demographic and detailed characterization work. *This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile