Context.The thirdGaiadata release (GaiaDR3) contains, beyond the astrometry and photometry, dispersed light for hundreds of millions of sources from theGaiaprism spectra (BP and RP) and the spectrograph (RVS). This data release opens a new window on the chemo-dynamical properties of stars in our Galaxy, essential knowledge for understanding the structure, formation, and evolution of the Milky Way.Aims.To provide insight into the physical properties of Milky Way stars, we used these data to produce a uniformly derived all-sky catalogue of stellar astrophysical parameters: atmospheric properties (T_eff, logg, [M/H], [α/Fe], activity index, emission lines, and rotation), 13 chemical abundance estimates, evolution characteristics (radius, age, mass, and bolometric luminosity), distance, and dust extinction.Methods.We developed the astrophysical parameter inference system (Apsis) pipeline to infer astrophysical parameters ofGaiaobjects by analysing their astrometry, photometry, BP/RP, and RVS spectra. We validate our results against those from other works in the literature, including benchmark stars, interferometry, and asteroseismology. Here we assess the stellar analysis performance from Apsis statistically.Results.We describe the quantities we obtained, including the underlying assumptions and the limitations of our results. We provide guidance and identify regimes in which our parameters should and should not be used.Conclusions.Despite some limitations, this is the most extensive catalogue of uniformly inferred stellar parameters to date. They compriseT_eff, logg, and [M/H] (470 million using BP/RP, 6 million using RVS), radius (470 million), mass (140 million), age (120 million), chemical abundances (5 million), diffuse interstellar band analysis (half a million), activity indices (2 million), Hαequivalent widths (200 million), and further classifications of spectral types (220 million) and emission-line stars (50 thousand). More precise and detailed astrophysical parameters based on epoch BP, RP, and RVS spectrophotometry are planned for the nextGaiadata release.