Abstract We study the sizes, angular momenta, and morphologies of high-redshift galaxies, using an update of the meraxes semi-analytic galaxy evolution model. Our model successfully reproduces a range of observations from redshifts z = 0–10. We find that the effective radius of a galaxy disc scales with ultraviolet (UV) luminosity as $R_\mathrm{ e}∝ L_{\textrm{UV}}^{0.33}$ at z = 5–10, and with stellar mass as $R_e∝ M_* ^{0.24}$ at z = 5 but with a slope that increases at higher redshifts. Our model predicts that the median galaxy size scales with redshift as Re ∝ (1 + z)−m, where m = 1.98 ± 0.07 for galaxies with (0.3–1)$L^* _{z=3}$ and m = 2.15 ± 0.05 for galaxies with (0.12–0.3)$L^* _{z=3}$. We find that the ratio between stellar and halo specific angular momentum is typically less than 1 and decreases with halo and stellar mass. This relation shows no redshift dependence, while the relation between specific angular momentum and stellar mass decreases by ∼0.5 dex from z = 7 to z = 2. Our model reproduces the distribution of local galaxy morphologies, with bulges formed predominantly through galaxy mergers for low-mass galaxies, disc-instabilities for galaxies with M* ≃ 1010–$10^{11.5}\, \mathrm{M}_⊙$, and major mergers for the most massive galaxies. At high redshifts, we find galaxy morphologies that are predominantly bulge-dominated.