  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} $G\leq20$
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 21\farcs06. 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://zenodo.org/record/6837642#.YtEgjy8RrzI.
