The ALESS survey has followed-up a sample of 122 sub-millimeter sources in the Extended Chandra Deep Field South at 870 \mu m with ALMA , allowing to pinpoint the positions of sub-millimeter galaxies ( SMGs ) to \sim 0.3 arcsec and to find their precise counterparts at different wavelengths . This enabled the first compilation of the multi-wavelength spectral energy distributions ( SEDs ) of a statistically reliable survey of SMGs . In this paper , we present a new calibration of the magphys SED modelling code that is optimized to fit these ultraviolet-to-radio SEDs of z > 1 star-forming galaxies using an energy balance technique to connect the emission from stellar populations , dust attenuation and dust emission in a physically consistent way . We derive statistically and physically robust estimates of the photometric redshifts and physical parameters ( such as stellar masses , dust attenuation , star formation rates , dust masses ) for the ALESS SMGs . We find that the ALESS SMGs have a median stellar mass M _ { \ast } = ( 8.9 \pm 0.1 ) \times 10 ^ { 10 } ~ { } M _ { \odot } , median star formation rate SFR = 280 \pm 70 ~ { } M _ { \odot } \mathrm { yr } ^ { -1 } , median overall V -band dust attenuation A _ { V } = 1.9 \pm 0.2 mag , median dust mass M _ { \mathrm { dust } } = ( 5.6 \pm 1.0 ) \times 10 ^ { 8 } ~ { } M _ { \odot } , and median average dust temperature T _ { \mathrm { dust } } \simeq 40 K. We find that the average intrinsic spectral energy distribution of the ALESS SMGs resembles that of local ultra-luminous infrared galaxies in the infrared range , but the stellar emission of our average SMG is brighter and bluer , indicating lower dust attenuation , possibly because they are more extended . We explore how the average SEDs vary with different parameters ( redshift , sub-millimeter flux , dust attenuation and total infrared luminosity ) , and we provide a new set of SMG templates that can be used to interpret other SMG observations . To put the ALESS SMGs into context , we compare their stellar masses and star formation rates with those of less actively star-forming galaxies at the same redshifts . We find that , at z \simeq 2 , about half of the SMGs lie above the star-forming main sequence ( with star formation rates three times larger than normal galaxies of the same stellar mass ) , while half are consistent with being at the high-mass end of the main sequence . At higher redshifts ( z \simeq 3.5 ) , the SMGs tend to have higher star formation rates and stellar masses , but the fraction of SMGs that lie significantly above the main sequence decreases to less than a third .