Blue horizontal-branch stars evolve from low-mass stars that have completed their main-sequence lifetimes and undergone a helium flash at the end of their red-giant phase. As such, blue horizontal-branch stars are very old objects that can be used as markers in studies of the Galactic structure and formation history. To create a clean sky catalogue of blue horizontal-branch stars, we cross-matched the Gaia data release 2 (DR2) dataset with existing reference catalogues to define selection criteria based on Gaia DR2parameters. Following the publication of Gaia early data release 3 (EDR3), these methods were verified and subsequently applied to this latest release. Previous catalogues of blue horizontal-branch stars were developed using spectral analyses or were restricted to individual globular clusters. The purpose of this catalogue is to identify a set of blue horizontal-branch star candidates that have been selected using photometric and astrometric observations and exhibits a low contamination rate. This has been deemed important as the success of the Gaia mission has changed the way that targets are selected for large-scale spectroscopic surveys, meaning that far fewer spectra will be acquired for blue horizontal-branch stars in the future unless they are specifically targeted. We cross-matched reference blue horizontal-branch datasets with the Gaia DR2 database and defined two sets of selection criteria. Firstly, in Gaia DR2 - colour and absolute G magnitude space, and secondly, in Gaia DR2 - colour and reduced proper motion space. The main-sequence contamination in both subsets of the catalogue was reduced, at the expense of completeness, by concentrating on the Milky Way's Galactic halo, where relatively young main-sequence stars were not expected. The entire catalogue is limited to those stars with no apparent neighbours within 5 arcsec. These methods were verified and subsequently applied to theGaia Early Data Release 3 (EDR3). We present a catalogue, based on Gaia EDR3, of 57377 blue horizontal-branch stars. The Gaia EDR3 parallax was used in selecting 16794 candidates and the proper motions were used to identify a further 40583 candidates.