Context.Blue (BP) and Red (RP) Photometer low-resolution spectral data are one of the exciting new products inGaiaData Release 3 (GaiaDR3). These data have also been used to derive astrometry and integrated photometry inGaiaEarly Data Release 3 and astrophysical parameters and Solar System object reflectance spectra inGaiaDR3.Aims.In this paper, we give an overview of the processing techniques that allow raw satellite data of multiple transits per source to be converted into combined spectra calibrated to an internal reference system, resulting in low-resolution BP and RP mean spectra. We describe how we overcome challenges due to the complexity of the on-board instruments and to the various observation strategies. Furthermore, we show highlights from our scientific validation of the results. This work covers the internal calibration of BP/RP spectra to a self-consistent mean instrument, while the calibration of the BP/RP spectra to the absolute reference system of physical flux and wavelength is covered by one of the accompanyingGaiaDR3 papers.Methods.We calibrate about 65 billion individual transit spectra onto the same mean BP/RP instrument through a series of calibration steps, including background subtraction, calibration of the CCD geometry, and an iterative procedure for the calibration of CCD efficiency as well as variations of the line-spread function and dispersion across the focal plane and in time. The calibrated transit spectra are then combined for each source in terms of an expansion into continuous basis functions. We discuss the configuration of these basis functions.Results.Time-averaged mean spectra covering the optical to near-infrared wavelength range [330, 1050] nm are published for approximately 220 million objects. Most of these are brighter thanG = 17.65 but some BP/RP spectra are published for sources down toG = 21.43. Their signal-to-noise ratio (S/N) varies significantly over the wavelength range covered, and with magnitude and colour of the observed objects, with sources aroundG = 15 having a S/N above 100 in some wavelength ranges. The top-quality BP/RP spectra are achieved for sources with magnitudes 9 < G < 12, with S/N reaching 1000 in the central part of the RP wavelength range. Scientific validation suggests that the internal calibration was generally successful. However, there is some evidence for imperfect calibrations at the bright endG < 11, where calibrated BP/RP spectra can exhibit systematic flux variations that exceed their estimated flux uncertainties. We also report that, due to long-range noise correlations, BP/RP spectra can exhibit wiggles when sampled in pseudo-wavelength.Conclusions.TheGaiaDR3 data products are the expansion coefficients and corresponding covariance matrices for BP and RP separately. Users are encouraged to work with the data in this format, with full covariance information showing that correlations between coefficients are typically very low. Documentation and instructions on how to access and use BP/RP spectral data from the archive are also provided.