Context.RR Lyrae stars are excellent tracers of the oldest stars (ages ≳ 9–10 Gyr) and standard candles for measuring the distance to stellar systems that are mainly composed of an old stellar population. TheGaiaThird Data Release (DR3) publishes a catalogue of full-sky RR Lyrae stars observed during the initial 34 months of science operations. They were processed through the Specific Object Study (SOS) pipeline, which was developed to validate and characterise Cepheids and RR Lyrae stars (SOS Cep&RRL) observed byGaia.Aims.The main steps of the SOS Cep&RRL pipeline are described in the documentation and papers accompanying previousGaiadata releases. For DR3, the pipeline was modified in its process: in addition to theGaiamultiband (G,G_BP,G_RP) time-series photometry, the epoch radial velocities measured for RR Lyrae and Cepheids with the Radial Velocity Spectrometer (RVS) on boardGaiawere also processed through the pipeline.Methods.The SOS Cep&RRL validation of DR3 candidate RR Lyrae stars relies on diagnostics tools that include the period versusG-amplitude diagram and the period versusϕ₂₁andϕ₃₁parameters of theGlight-curve Fourier decomposition, as defined by a reference sample of bona fide RR Lyrae stars known in the literature (that we named Gold Sample). Great care was devoted to building a large and pure Gold Sample comprising more than 200 000 RR Lyrae stars. The SOS processing led to an initial catalogue of 271779 RR Lyrae stars that are listed in thevari_rrlyraetable of the DR3 archive. A thorough cleaning procedure was then performed to produce a final catalogue of SOS-confirmed DR3 RR Lyrae stars by dropping sources that clearly are contaminants or have an uncertain classification.Results.Multiband time-series photometry and characterisation are published inGaiaDR3 for a clean, validated sample of 270 905 RR Lyrae stars (174 947 fundamental-mode, 93 952 first-overtone, and 2006 double-mode RR Lyrae) that were confirmed and fully characterised by the SOS Cep&RRL pipeline. They are distributed throughout the sky, including variables in 95 globular clusters and 25 Milky Way (MW) companions (the Magellanic Clouds, seven dwarf spheroidal galaxies, and 16 ultra-faint dwarf satellites of the MW). RVS time-series radial velocities are also published for 1096 RR Lyrae and 799 Cepheids of different types (classical, anomalous, and type II Cepheids). Of the 270 905 DR3 RR Lyrae stars, 200 294 are already known in the literature (Gold Sample) and 70 611 are new discoveries byGaia, to the best of our knowledge. An estimate of the interstellar absorption is published for 142 660 fundamental-mode RR Lyrae stars from a relation based on theG-band amplitude, the (G−G_RP) colour and the pulsation period. Metallicities derived from the Fourier parameters of the light curves are also released for 133 559 RR Lyrae stars.Conclusions.The finalGaiaDR3 catalogue of confirmed RR Lyrae stars almost doubles the DR2 RR Lyrae catalogue. An increase in statistical significance, a better characterisation of the RR Lyrae pulsational and astrophysical parameters, and the improved astrometry published withGaiaEDR3 make the SOS Cep&RRL DR3 sample the largest, most homogeneous, and parameter-richest catalogue of all-sky RR Lyrae stars published so far in the magnitude range from ⟨G⟩=7.64 mag (the magnitude of RR Lyr itsef, the class prototype) to ⟨G⟩=21.14 mag (the faintest RR Lyrae in the catalogue).