The Gaia Galactic survey mission is designed and optimized to obtain astrometry, photometry, and spectroscopy of nearly two billion stars in our Galaxy. Yet as an all-sky multi-epoch survey, Gaia also observes several million extragalactic objects down to a magnitude of G ∼ 21 mag. Due to the nature of the Gaia onboard-selection algorithms, these are mostly point-source-like objects. Using data provided by the satellite, we have identified quasar and galaxy candidates via supervised machine learning methods, and estimate their redshifts using the low resolution BP/RP spectra. We further characterise the surface brightness profiles of host galaxies of quasars and of galaxies from pre-defined input lists. Here we give an overview of the processing of extragalactic objects, describe the data products in Gaia DR3, and analyse their properties. Two integrated tables contain the main results for a high completeness, but low purity (50−70%), set of 6.6 million candidate quasars and 4.8 million candidate galaxies. We provide queries that select purer sub-samples of these containing 1.9 million probable quasars and 2.9 million probable galaxies (both ∼95% purity). We also use high quality BP/RP spectra of 43 thousand high probability quasars over the redshift range 0.05−4.36 to construct a composite quasar spectrum spanning restframe wavelengths from 72−1000 nm.Full Table 8 is only available at the CDS via anonymous ftp to cdsarc.cds.unistra.fr (ftp://188.8.131.52) or via https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/674/A41.