The Tycho-Gaia Astrometric Solution (TGAS) subset of the first Gaia catalogue contains an unprecedented sample of proper motions and parallaxes for two million stars brighter than G~12 mag. We take advantage of the full astrometric solution available for those stars to identify the members of known open clusters and compute mean cluster parameters using either TGAS or UCAC4 proper motions, and TGAS parallaxes. We apply an unsupervised membership assignment procedure to select high probability cluster members, we use a Bayesian/MCMC technique to fit stellar isochrones to the observed 2MASS JHK magnitudes of the member stars and derive cluster parameters (age, metallicity, extinction, distance modulus), and we combine TGAS data with spectroscopic radial velocities to compute full Galactic orbits. We obtain mean astrometric parameters (proper motions and parallaxes) for 128 clusters closer than about 2kpc, and cluster parameters from isochrone fitting for 26 of them located inside 1kpc from us. We show the orbital parameters obtained from integrating 36 orbits in a Galactic potential.