We present two catalogues of active galactic nucleus (AGN) candidates selected from the latest data of two all-sky surveys -- Data Release 2 (DR2) of the emph{Gaia} mission and the unWISE catalogue of the emph{Wide-field Infrared Survey Explorer} (emph{WISE}). We train a random forest classifier to predict the probability of each source in the emph{Gaia}-unWISE joint sample being an AGN, $P_{rm RF}$, based on emph{Gaia} astrometric and photometric measurements and unWISE photometry. The two catalogues, which we designate C75 and R85, are constructed by applying different $P_{rm RF}$ threshold cuts to achieve an overall completeness of 75% ($approx$90% at emph{Gaia} $Gleq20$ mag) and reliability of 85% respectively. The C75 (R85) catalogue contains 2,734,464 (2,182,193) AGN candidates across the effective 36,000 deg$^2$ sky, of which $approx$0.91 (0.52) million are new discoveries. Photometric redshifts of the AGN candidates are derived by a random forest regressor using emph{Gaia} and emph{WISE} magnitudes and colours. The estimated overall photometric redshift accuracy is 0.11. Cross-matching the AGN candidates with a sample of known bright cluster galaxies, we identify a high-probability strongly-lensed AGN candidate system, SDSS,J1326$+$4806, with a large image separation of 21farcs06. All the AGN candidates in our catalogues will have $sim$5-year long light curves from emph{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 ones in the southern hemisphere. The C75 catalogue can be downloaded at https://www.ast.cam.ac.uk/~ypshu/AGN_Catalogues.html.
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