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This paper is the second in a pair of papers presenting data release 1 (DR1) of the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS), the largest single open-time key project carried out with the Herschel Space Observatory. The H-ATLAS is a wide-area imaging survey carried out in five photometric bands at 100, 160, 250, 350 and 500 mu m covering a total area of 600 deg2. In this paper, we describe the identification of optical counterparts to submillimetre sources in DR1, comprising an area of 161 deg2 over three equatorial fields of roughly 12 x 4.5 deg centred at 9(h), 12(h) and 14.(h)5, respectively. Of all the H-ATLAS fields, the equatorial regions benefit from the greatest overlap with current multi-wavelength surveys spanning ultraviolet (UV) to mid-infrared regimes, as well as extensive spectroscopic coverage. We use a likelihood ratio technique to identify Sloan Digital Sky Survey counterparts at r < 22.4 for 250-mu m-selected sources detected at >= 4 sigma (approximate to 28 mJy). We find 'reliable' counterparts (reliability R >= 0.8) for 44 835 sources (39 per cent), with an estimated completeness of 73.0 per cent and contamination rate of 4.7 per cent. Using redshifts and multi-wavelength photometry from GAMA and other public catalogues, we show that H-ATLAS-selected galaxies at z < 0.5 span a wide range of optical colours, total infrared (IR) luminosities and IR/UV ratios, with no strong disposition towards mid-IR-classified active galactic nuclei in comparison with optical selection. The data described herein, together with all maps and catalogues described in the companion paper, are available from the H-ATLAS website at www.h-atlas.org.