Context. 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. Aims. 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 the fourth U.S. Naval Observatory CCD Astrograph Catalog (UCAC4) proper motions, and TGAS parallaxes. Methods. We apply an unsupervised membership assignment procedure to select high probability cluster members, we use a Bayesian/Markov Chain Monte Carlo technique to fit stellar isochrones to the observed 2MASS JHK_S 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. Results. We obtain mean astrometric parameters (proper motions and parallaxes) for 128 clusters closer than about 2 kpc, and cluster parameters from isochrone fitting for 26 of them located within a distance of 1 kpc from the Sun. We show the orbital parameters obtained from integrating 36 orbits in a Galactic potential.