This paper is the second in a pair of articles 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 600deg$^2$. In this paper we describe the identification of optical counterparts to submillimetre sources in DR1, comprising an area of 161 deg$^2$ over three equatorial fields of roughly 12$^circ$x4.5$^circ$ centred at 9$^h$, 12$^h$ and 14.5$^h$ 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 SDSS counterparts at r<22.4 for 250-$mu$m-selected sources detected at $geq$ 4$sigma$ ($approx$28mJy). We find `reliable counterparts (reliability R$geq$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 AGN in comparison with optical selection. The data described herein, together with all maps and catalogues described in the companion paper (Valiante et al. 2016), are available from the H-ATLAS website at www.h-atlas.org.
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