We present two catalogues of active galactic nucleus (AGN) candidates selected from the latest data of two all-sky surveys – Data Release 2 of the Gaia mission and the unWISE catalogue of the Wide-field Infrared Survey Explorer (WISE). We train a random forest classifier to predict the probability of each source in the Gaia–unWISE joint sample being an AGN, PRF, based on Gaia astrometric and photometric measurements and unWISE photometry. The two catalogues, which we designate C75 and R85, are constructed by applying different PRF threshold cuts to achieve an overall completeness of 75 per cent (≈90 per cent at GaiaG ≤ 20 mag) and reliability of 85 per cent, respectively. The C75 (R85) catalogue contains 2734 464 (2182 193) AGN candidates across the effective 36 000 deg2 sky, of which ≈0.91 (0.52) million are new discoveries. Photometric redshifts of the AGN candidates are derived by a random forest regressor using Gaia and WISE magnitudes and colours. The estimated overall photometric redshift accuracy is 0.11. Cross-matching the AGN candidates with a sample of known bright cluster galaxies, we identify a high-probability strongly lensed AGN candidate system, SDSS J1326+4806, with a large image separation of 21′′.06. All the AGN candidates in our catalogues will have ∼5-yr long light curves from Gaia by the end of the mission, and thus will be a great resource for AGN variability studies. Our AGN catalogues will also be helpful in AGN target selections for future spectroscopic surveys, especially those in the Southern hemisphere. The C75 catalogue can be downloaded at https://www.ast.cam.ac.uk/~ypshu/AGN_Catalogues.html.