The structure of crystalline interfaces plays an important role in solid-state reactions. The Al2O3/MgAl2O4/MgO system provides an ideal model system for investigating the mechanisms underlying the migration of interfaces during interface reaction. MgAl2O4 layers have been grown between Al2O3 and MgO, and the atomic structure of Al2O3/MgAl2O4 interfaces at different growth stages was characterized using aberration-corrected scanning transmission electron microscopy. The oxygen sublattice transforms from hexagonal close-packed (hcp) stacking in Al2O3 to cubic close-packed (ccp) stacking in MgAl2O4. Partial dislocations associated with steps are observed at the interface. At the reaction-controlled early growth stages, such partial dislocations coexist with the edge dislocations. However, at the diffusion-controlled late growth stages, such partial dislocations are dominant. The observed structures indicate that progression of the Al2O3/MgAl2O4 interface into Al2O3 is accomplished by the glide of partial dislocations accompanied by the exchange of Al3+ and Mg2+ cations. The interface migration may be envisaged as a plane-by-plane zipper-like motion, which repeats along the interface facilitating its propagation. MgAl2O4 grains can adopt two crystallographic orientations with a twinning orientation relationship, and grow by dislocations gliding in opposite directions. Where the oppositely propagating partial dislocations and interface steps meet, interlinked twin boundaries and incoherent {Sigma}3 grain boundaries form. The newly grown MgAl2O4 grains compete with each other, leading to a growth-selection and successive coarsening of the MgAl2O4 grains. This understanding could help to interpret the interface reaction or phase transformation of a wide range of materials that exhibit a similar hcp/ccp transition.