The results of the first extragalactic gamma-ray survey by the High Energy Stereoscopic System (H.E.S.S.) are presented. The survey comprises 2720 hours of very high-energy gamma-ray observations of the extragalactic sky, recorded with H.E.S.S. from 2004 up to the end of 2012. These data have been re-analysed using a common consistent set of up-to-date data calibration and analysis tools. From this analysis, a list of 23 detected objects, predominantly blazars, was obtained. This catalogue was assessed in terms of the source class populations that it contains. The level of source parameter bias for the blazar sources, probed by this observational dataset, was evaluated using Monte-Carlo simulations. Spectral results obtained with the H.E.S.S. data were compared with the Fermi-LAT catalogues to present the full gamma-ray picture of the detected objects. Lastly, this unique dataset was used to assess the contribution of BL Lacertae objects and flat-spectrum radio quasars to the extragalactic gamma-ray background light at several hundreds of gigaelectronvolts. These results are accompanied by the release of the high-level data to the astrophysical community.