We identify and investigate the nature of the 20 brightest 250 { \mu m } sources detected by the Balloon-borne Large Aperture Submillimetre Telescope ( BLAST ) within the central 150 arcmin ^ { 2 } of the GOODS-South field . Aided by the available deep VLA 1.4 GHz radio imaging , reaching S _ { 1.4 } \simeq 40 { \mu Jy } ( 4- \sigma ) , we have identified radio counterparts for 17/20 of the 250 { \mu m } sources . The resulting enhanced positional accuracy of \simeq 1 arcsec has then allowed us to exploit the deep optical ( HST ) , near-infrared ( VLT ) and mid-infrared ( Spitzer ) imaging of GOODS-South to establish secure galaxy counterparts for the 17 radio-identified sources , and plausible galaxy candidates for the 3 radio-unidentified sources . Confusion is a serious issue for this deep BLAST 250 { \mu m } survey , due to the large size of the beam . Nevertheless , we argue that our chosen counterparts are significant , and often dominant contributors to the measured BLAST flux densities . For all of these 20 galaxies we have been able to determine spectroscopic ( 8 ) or photometric ( 12 ) redshifts . The result is the first near-complete redshift distribution for a deep 250 { \mu m } -selected galaxy sample . This reveals that 250 { \mu m } surveys reaching detection limits of \simeq 40 mJy have a median redshift z \simeq 1 , and contain not only low-redshift spirals/LIRGs , but also the extreme z \simeq 2 dust-enshrouded starburst galaxies previously discovered at sub-millimetre wavelengths . Inspection of the LABOCA 870 { \mu m } imaging of GOODS-South yields detections of \simeq 1 / 3 of the proposed BLAST sources ( all at z > 1.5 ) , and reveals 250/870 { \mu m } flux-density ratios consistent with a standard 40 K modified black-body fit with a dust emissivity index \beta = 1.5 . Based on their IRAC colours , we find that virtually all of the BLAST galaxy identifications appear better described as analogues of the M82 starburst galaxy , or Sc star-forming discs rather than highly obscured ULIRGs . This is perhaps as expected at low redshift , where the 250 \mu m BLAST selection function is biased towards spectral energy distributions which peak longward of \lambda _ { rest } = 100 { \mu m } . However , it also appears largely true at z \simeq 2 .