Context. Gaia Data Release 3 contains astrometry and photometry results for about 1.8 billion sources based on observations collected by the European Space Agency (ESA) Gaia satellite during the first 34 months of its operational phase (the same period covered Gaia early Data Release 3; Gaia EDR3). Low-resolution spectra for 220 million sources are one of the important new data products included in this release. Aims. In this paper, we focus on the external calibration of low-resolution spectroscopic content, describing the input data, algorithms, data processing, and the validation of the results. Particular attention is given to the quality of the data and to a number of features that users may need to take into account to make the best use of the catalogue. Methods. We calibrated an instrument model to relate mean Gaia spectra to the corresponding spectral energy distributions (SEDs) using an extended set of calibrators: this includes modelling of the instrument dispersion relation, transmission, and line spread functions. Optimisation of the model is achieved through total least-squares regression, accounting for errors in Gaia and external spectra.Results. The resulting instrument model can be used for forward modelling of Gaia spectra or for inverse modelling of externally calibrated spectra in absolute flux units. Conclusions. The absolute calibration derived in this paper provides an essential ingredient for users of BP/RP spectra. It allows users to connect BP/RP spectra to absolute fluxes and physical wavelengths.