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Gaia DR3 publishes a catalogue of full-sky RR Lyrae stars (RRLs) observed during the initial 34 months of science operations, that were processed through the Specific Object Study (SOS) pipeline for Cepheids and RRLs (SOS Cep&RRL) observed by Gaia. The SOS Cep&RRL validation of DR3 candidate RRLs relies on tools that include the Period (P) G-amplitude diagram and the P-phi21 and -phi31 parameters of the G light curve Fourier decomposition, based on a sample of bona fide known RRLs (Gold Sample). The SOS processing led to a catalogue of 271779 RRLs listed in the vari_rrlyrae table of DR3. By dropping sources that clearly are contaminants, or have an uncertain classification we produce the final catalogue of SOS-confirmed DR3 RRLs containing 270905 sources (174947 fundamental mode, 93952 first overtone and 2006 double-mode RRLs) confirmed and fully characterised by the SOS Cep&RRL pipeline. They are distributed all over the sky, including 95 globular clusters and 25 Milky Way companions. RVS time series radial velocities are also published for 1096 RRLs and 799 Cepheids. Of the 270905 DR3 RRLs, 200294 are already known in the literature and 70611 are, to the best of our knowledge, new discoveries by Gaia. An estimate of the interstellar absorption is published for 142660 fundamental-mode RRLs from a relation based on the G-band amplitude and the pulsation period. Metallicities derived from the Periods and the phi31 Fourier parameters of the G-light curves are also released for 133559 RRLs. The final Gaia DR3 catalogue of confirmed RRLs almost doubles the DR2 RRLs catalogue. An increase of statistical significance, a better characterization of the RRLs pulsational and astrophysical parameters, and the improved astrometry published with Gaia EDR3, make the SOS Cep&RRL DR3 sample, the largest, most homogeneous and parameter-rich catalogue of All-Sky RRLs published so far.