The Transiting Exoplanet Survey Satellite (TESS) will provide high-precision time series photometry for millions of stars with at least a half-hour cadence. Of particular interest are the circular regions of 12° radius centred around the ecliptic poles that will be observed continuously for a full year. Spectroscopic stellar parameters are desirable to characterize and select suitable targets for TESS, whether they are focused on exploring exoplanets, stellar astrophysics or Galactic archaeology. Here, we present spectroscopic stellar parameters (Teff, log g, [Fe/H], v sin i, vmicro) for about 16 000 dwarf and subgiant stars in TESS' southern continuous viewing zone. For almost all the stars, we also present Bayesian estimates of stellar properties including distance, extinction, mass, radius and age using theoretical isochrones. Stellar surface gravity and radius are made available for an additional set of roughly 8500 red giants. All our target stars are in the range 10 < V < 13.1. Among them, we identify and list 227 stars belonging to the Large Magellanic Cloud. The data were taken using the High Efficiency and Resolution Multi-Element Spectrograph (HERMES; R ~ 28 000) at the Anglo-Australian Telescope as part of the TESS-HERMES survey. Comparing our results with the TESS Input Catalogue (TIC) shows that the TIC is generally efficient in separating dwarfs and giants, but it has flagged more than 100 cool dwarfs (Teff < 4800 K) as giants, which ought to be high-priority targets for the exoplanet search. The catalogue can be accessed via http://www.physics.usyd.edu.au/tess-hermes/, or atMikulski Archive for Space Telescopes (MAST).