We report the results of the counterpart identification and a detailed analysis of the physical properties of the 48 sources discovered in our deep 1.1-mm wavelength imaging survey of the Great Observatories Origins Deep Survey-South (GOODS-S) field using the AzTEC instrument on the Atacama Submillimeter Telescope Experiment. One or more robust or tentative counterpart candidate is found for 27 and 14 AzTEC sources, respectively, by employing deep radio continuum, Spitzer/Multiband Imaging Photometer for Spitzer and Infrared Array Camera, and Large APEX Bolometer Camera 870 μm data. Five of the sources (10 per cent) have two robust counterparts each, supporting the idea that these galaxies are strongly clustered and/or heavily confused. Photometric redshifts and star formation rates (SFRs) are derived by analysing ultraviolet(UV)-to-optical and infrared(IR)-to-radio spectral energy distributions (SEDs). The median redshift of zmed∼ 2.6 is similar to other earlier estimates, but we show that 80 per cent of the AzTEC–GOODS sources are at z≥ 2, with a significant high-redshift tail (20 per cent at z≥ 3.3). Rest-frame UV and optical properties of AzTEC sources are extremely diverse, spanning 10 mag in the i- and K-band photometry (a factor of 104 in flux density) with median values of i= 25.3 and K= 22.6 and a broad range of red colour (i−K= 0–6) with an average value of i−K≈ 3. These AzTEC sources are some of the most luminous galaxies in the rest-frame optical bands at z≥ 2, with inferred stellar masses M*= (1–30) × 1010 M⊙ and UV-derived SFRs of SFRUV≳ 101-3 M⊙ yr−1. The IR-derived SFR, 200–2000 M⊙ yr−1, is independent of z or M*. The resulting specific star formation rates, SSFR ≈ 1–100 Gyr−1, are 10–100 times higher than similar mass galaxies at z= 0, and they extend the previously observed rapid rise in the SSFR with redshift to z= 2–5. These galaxies have a SFR high enough to have built up their entire stellar mass within their Hubble time. We find only marginal evidence for an active galactic nucleus (AGN) contribution to the near-IR and mid-IR SEDs, even among the X-ray detected sources, and the derived M* and SFR show little dependence on the presence of an X-ray bright AGN.