ABSTRACT The properties of young star clusters formed within a galaxy are thought to vary in different interstellar medium conditions, but the details of this mapping from galactic to cluster scales are poorly understood due to the large dynamic range involved in galaxy and star cluster formation. We introduce a new method for modelling cluster formation in galaxy simulations: mapping giant molecular clouds (GMCs) formed self-consistently in a FIRE-2 magnetohydrodynamic galaxy simulation on to a cluster population according to a GMC-scale cluster formation model calibrated to higher resolution simulations, obtaining detailed properties of the galaxy’s star clusters in mass, metallicity, space, and time. We find $\sim 10{{\ \rm per\ cent}}$ of all stars formed in the galaxy originate in gravitationally bound clusters overall, and this fraction increases in regions with elevated Σgas and ΣSFR, because such regions host denser GMCs with higher star formation efficiency. These quantities vary systematically over the history of the galaxy, driving variations in cluster formation. The mass function of bound clusters varies – no single Schechter-like or power-law distribution applies at all times. In the most extreme episodes, clusters as massive as 7 × 106 M⊙ form in massive, dense clouds with high star formation efficiency. The initial mass–radius relation of young star clusters is consistent with an environmentally dependent 3D density that increases with Σgas and ΣSFR. The model does not reproduce the age and metallicity statistics of old ($\gt 11\rm Gyr$) globular clusters found in the Milky Way, possibly because it forms stars more slowly at z > 3.