The AMBRE project is a collaboration between the European Southern Observatory (ESO) and the Observatoire de la Cote d'Azur (OCA). It has been established to determine the stellar atmospheric parameters (effective temperature, surface gravity, global metallicities and abundance of alpha-elements over iron) of the archived spectra of four ESO spectrographs. The analysis of the ESO:HARPS archived spectra is presented. The sample being analysed (AMBRE:HARPS) covers the period from 2003 to 2010 and is comprised of 126688 scientific spectra corresponding to 17218 different stars. For the analysis of the spectral sample, the automated pipeline developed for the analysis of the AMBRE:FEROS archived spectra has been adapted to the characteristics of the HARPS spectra. Within the pipeline, the stellar parameters are determined by the MATISSE algorithm, developed at OCA for the analysis of large samples of stellar spectra in the framework of galactic archaeology. In the present application, MATISSE uses the AMBRE grid of synthetic spectra, which covers FGKM-type stars for a range of gravities and metallicities. We first determined the radial velocity and its associated error for the ~15% of the AMBRE:HARPS spectra, for which this velocity had not been derived by the ESO:HARPS reduction pipeline. The stellar atmospheric parameters and the associated chemical index [alpha/Fe] with their associated errors have then been estimated for all the spectra of the AMBRE:HARPS archived sample. Based on quality criteria, we accepted and delivered the parameterisation of ~71% of the total sample to ESO. These spectra correspond to ~10706 stars; each are observed between one and several hundred times. This automatic parameterisation of the AMBRE:HARPS spectra shows that the large majority of these stars are cool main-sequence dwarfs with metallicities greater than -0.5 dex.