We present a catalogue of 4098 photometrically selected galaxy clusters with a median redshift 〈z〉= 0.32 in the 270 deg2‘Stripe 82’ region of the Sloan Digital Sky Survey (SDSS), covering the celestial equator in the Southern Galactic Cap (−50° < α < 59°, |δ| ≤ 125). Owing to the multi-epoch SDSS coverage of this region, the ugriz photometry is ∼2 mag deeper than single scans within the main SDSS footprint. We exploit this to detect clusters of galaxies using an algorithm that searches for statistically significant overdensities of galaxies in a Voronoi tessellation of the projected sky. 32 per cent of the clusters have at least one member with a spectroscopic redshift from existing public data (SDSS Data Release 7, 2SLAQ and WiggleZ), and the remainder have a robust photometric redshift (accurate to ∼5–9 per cent at the median redshift of the sample). The weighted average of the member galaxies’ redshifts provides a reasonably accurate estimate of the cluster redshift. The cluster catalogue is publicly available for exploitation by the community to pursue a range of science objectives. In addition to the cluster catalogue, we provide a linked catalogue of 18 295 V≤ 21-mag quasar sightlines with impact parameters within ≤3 Mpc of the cluster cores selected from the catalogue of Veron-Cetty & Veron (2010). The background quasars cover 0.25 < z < 2, where Mg ii absorption-line systems associated with the clusters are detectable in optical spectra.