We present the data release paper for the Galaxy Zoo: Hubble (GZH) project. This is the third phase in a large effort to measure reliable, detailed morphologies of galaxies by using crowdsourced visual classifications of colour-composite images. Images in GZH were selected from various publicly released Hubble Space Telescope legacy programmes conducted with the Advanced Camera for Surveys, with filters that probe the rest-frame optical emission from galaxies out to z ∼ 1. The bulk of the sample is selected to have mI814W < 23.5, but goes as faint as mI814W < 26.8 for deep images combined over five epochs. The median redshift of the combined samples is 〈z〉 = 0.9 ± 0.6, with a tail extending out to z ≃ 4. The GZH morphological data include measurements of both bulge- and disc-dominated galaxies, details on spiral disc structure that relate to the Hubble type, bar identification, and numerous measurements of clump identification and geometry. This paper also describes a new method for calibrating morphologies for galaxies of different luminosities and at different redshifts by using artificially redshifted galaxy images as a baseline. The GZH catalogue contains both raw and calibrated morphological vote fractions for 119 849 galaxies, providing the largest data set to date suitable for large-scale studies of galaxy evolution out to z ∼ 1.