The Transiting Exoplanet Survey Satellite (TESS) will search for planets transiting bright and nearby stars. TESS has been selected by NASA for launch in 2017 as an Astrophysics Explorer mission. The spacecraft will be placed into a highly elliptical 13.7-day orbit around the Earth. During its 2-year mission, TESS will employ four wide-field optical charge-coupled device cameras to monitor at least 200,000 main-sequence dwarf stars with IC≈4-13 for temporary drops in brightness caused by planetary transits. Each star will be observed for an interval ranging from 1 month to 1 year, depending mainly on the star's ecliptic latitude. The longest observing intervals will be for stars near the ecliptic poles, which are the optimal locations for follow-up observations with the James Webb Space Telescope. Brightness measurements of preselected target stars will be recorded every 2 min, and full frame images will be recorded every 30 min. TESS stars will be 10 to 100 times brighter than those surveyed by the pioneering Kepler mission. This will make TESS planets easier to characterize with follow-up observations. TESS is expected to find more than a thousand planets smaller than Neptune, including dozens that are comparable in size to the Earth. Public data releases will occur every 4 months, inviting immediate community-wide efforts to study the new planets. The TESS legacy will be a catalog of the nearest and brightest stars hosting transiting planets, which will endure as highly favorable targets for detailed investigations.