The Gaia-ESO Survey (GES) observed many open clusters as part of its programme to spectroscopically characterise the various Milky Way populations. GES spectroscopy and Gaia astrometry from its second data release are used here to assign membership probabilities to targets towards 32 open clusters with ages from 1-3800 Myr, based on maximum likelihood modelling of the 3D kinematics of the cluster and field populations. From a parent catalogue of 14398 individual targets, 5033 stars with uniformly determined 3D velocities, $Teff$, $\log g$ and chemistry are assigned cluster membership with probability $>0.9$, and with an average probability of 0.991. The robustness of the membership probabilities is demonstrated using independent membership criteria (lithium and parallax) in two of the youngest clusters. The addition of radial velocities improves membership discrimination over proper motion selection alone, especially in more distant clusters. The kinematically-selected nature of the membership lists, independent of photometry and chemistry, makes the catalogue a valuable resource for testing stellar evolutionary models and investigating the time evolution of various parameters.