We present spectroscopic redshifts of S(870)>2mJy submillimetre galaxies (SMGs) which have been identified from the ALMA follow-up observations of 870um detected sources in the Extended Chandra Deep Field South (the ALMA-LESS survey). We derive spectroscopic redshifts for 52 SMGs, with a median of z=2.4+/-0.1. However, the distribution features a high redshift tail, with ~25% of the SMGs at z>3. Spectral diagnostics suggest that the SMGs are young starbursts, and the velocity offsets between the nebular emission and UV ISM absorption lines suggest that many are driving winds, with velocity offsets up to 2000km/s. Using the spectroscopic redshifts and the extensive UV-to-radio photometry in this field, we produce optimised spectral energy distributions (SEDs) using Magphys, and use the SEDs to infer a median stellar mass of M*=(6+/-1)x10^{10}Msol for our SMGs with spectroscopic redshifts. By combining these stellar masses with the star-formation rates (measured from the far-infrared SEDs), we show that SMGs (on average) lie a factor ~5 above the main-sequence at z~2. We provide this library of 52 template fits with robust and well-sampled SEDs available as a resource for future studies of SMGs, and also release the spectroscopic catalog of ~2000 (mostly infrared-selected) galaxies targeted as part of the spectroscopic campaign.
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