We investigate the multiwavelength properties of a sample of 450-μm-selected sources from the SCUBA-2 Cosmology Legacy Survey. A total of 69 sources were identified above 4σ in deep SCUBA-2 450-μm observations overlapping the UDS and COSMOS fields and covering 210 arcmin to a typical depth of σ = 1.5mJy. Reliable cross-identifications are found for 58 sources (84 per cent) in Spitzer and Hubble Space Telescope WFC3/IR data. The photometric redshift distribution (dN/dz) of 450-μm-selected sources is presented, showing a broad peak in the redshift range 1 <z <3 and a median of z = 1.4. Combining the SCUBA-2 photometry with Herschel SPIRE data from HerMES, the submm spectral energy distribution (SED) is examined via the use of modified blackbody fits, yielding aggregate values for the IR luminosity, dust temperature and emissivity of (L) = 10 L, (TD) = 42 ± 11K and (β) = 1.6 ± 0.5, respectively. The relationship between these SED parameters and the physical properties of galaxies is investigated, revealing correlations between TD and LIR and between βD and both stellar mass and effective radius. The connection between the star formation rate (SFR) and stellar mass is explored, with 24 per cent of 450-μm sources found to be 'starbursts', i.e. displaying anomalously high specific SFRs. However, both the number density and observed properties of these 'starburst' galaxies are found to be consistent with the population of normal star-forming galaxies.