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 programs conducted with the Advanced Camera for Surveys, with filters that probe the rest-frame optical emission from galaxies out to \(z \sim 1\). The bulk of the sample is selected to have \(m_{I814W} < 23.5\),but goes as faint as \(m_{I814W} < 26.8\) for deep images combined over 5 epochs. The median redshift of the combined samples is \(z = 0.9 \pm 0.6\), with a tail extending out to \(z \sim 4\). The GZH morphological data include measurements of both bulge- and disk-dominated galaxies, details on spiral disk 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 dataset to date suitable for large-scale studies of galaxy evolution out to \(z \sim 1\).