  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,
$T_{\rm eff}$, $\log g$ 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.
