Context. Gaia DR3 contains 1.8 billion sources with G -band photometry, 1.5 billion of which with G _BP and G _RP photometry, complemented by positions on the sky, parallax, and proper motion. The median number of field-of-view transits in the three photometric bands is between 40 and 44 measurements per source and covers 34 months of data collection.

Aims. We pursue a classification of Galactic and extra-galactic objects that are detected as variable by Gaia across the whole sky.

Methods. Supervised machine learning (eXtreme Gradient Boosting and Random Forest) was employed to generate multi-class, binary, and meta-classifiers that classified variable objects with photometric time series in the G , G _BP , and G _RP bands.

Results. Classification results comprise 12.4 million sources (selected from a much larger set of potential variable objects) and include about 9 million variable stars classified into 22 variability types in the Milky Way and nearby galaxies such as the Magellanic Clouds and Andromeda, plus thousands of supernova explosions in distant galaxies, 1 million active galactic nuclei, and almost 2.5 million galaxies. The identification of galaxies was made possible by the artificial variability of extended objects as detected by Gaia , so they were published in the galaxy_candidates table of the Gaia DR3 archive, separate from the classifications of genuine variability (in the vari_classifier_result table). The latter contains 24 variability classes or class groups of periodic and non-periodic variables (pulsating, eclipsing, rotating, eruptive, cataclysmic, stochastic, and microlensing), with amplitudes from a few milli-magnitudes to several magnitudes.