Exploration of the impact of synthetic material landscapes featuring tunable geometrical properties on physical processes is a research direction that is currently of great interest because of the outstanding phenomena that are continually being uncovered. Twistronics and the properties of wave excitations in moiré lattices are salient examples. Moiré patterns bridge the gap between aperiodic structures and perfect crystals, thus opening the door to the exploration of effects accompanying the transition from commensurate to incommensurate phases. Moiré patterns have revealed profound effects in graphene-based systems they are used to manipulate ultracold atoms6,7 and to create gauge potentials8, and are observed in colloidal clusters9. Recently, it was shown that photonic moiré lattices enable observation of the two-dimensional localization-to-delocalization transition of light in purely linear systems. Here, we employ moiré lattices optically induced in photorefractive nonlinear media to elucidate the formation of optical solitons under different geometrical conditions controlled by the twisting angle between the constitutive sublattices. We observe the formation of solitons in lattices that smoothly transition from fully periodic geometries to aperiodic ones, with threshold properties that are a pristine direct manifestation of flat-band physics.