Context. The β Pictoris moving group is one of the most well-known young associations in the solar neighbourhood and several members are known to host circumstellar discs, planets, and comets. Measuring its age precisely is essential to the study of several astrophysical processes, such as planet formation and disc evolution, which are strongly age-dependent.Aims. We aim to determine a precise and accurate dynamical traceback age for the β Pictoris moving group.Methods. Our sample combines the extremely precise Gaia DR2 astrometry with ground-based radial velocities measured in an homogeneous manner. We use an updated version of our algorithm to determine dynamical ages. The new approach takes into account a robust estimate of the spatial and kinematic covariance matrices of the association to improve the sample selection process and to perform the traceback analysis.Results. We estimate a dynamical age of 18.5−2.4+2.0 Myr for the β Pictoris moving group. We investigated the spatial substructure of the association at the time of birth and we propose the existence of a core of stars that is more concentrated. We also provide precise radial velocity measurements for 81 members of β Pic, including ten stars with the first determinations of their radial velocities.Conclusions. Our dynamical traceback age is three times more precise than previous traceback age estimates and, more importantly, for the first time it reconciles the traceback age with the most recent estimates of other dynamical, lithium depletion boundaries and isochronal ages. This has been possible thanks to the excellent astrometric and spectroscopic precisions, the homogeneity of our sample, and the detailed analysis of binaries and membership.< Réduire