Epitaxially fused colloidal quantum dot (QD) superlattices (epi-SLs) may enable a new class of semiconductors that combine the size-tunable photophysics of QDs with bulk-like electronic performance, but progress is hindered by a poor understanding of epi-SL formation and surface chemistry. Here we use X-ray scattering and correlative electron imaging and diffraction of individual SL grains to determine the formation mechanism of three-dimensional PbSe QD epi-SL films. We show that the epi-SL forms from a rhombohedrally distorted body centred cubic parent SL via a phase transition in which the QDs translate with minimal rotation (similar to 10 degrees) and epitaxially fuse across their {100} facets in three dimensions. This collective epitaxial transformation is atomically topotactic across the 10(3)-10(5) QDs in each SL grain. Infilling the epi-SLs with alumina by atomic layer deposition greatly changes their electrical properties without affecting the superlattice structure. Our work establishes the formation mechanism of three-dimensional QD epi-SLs and illustrates the critical importance of surface chemistry to charge transport in these materials.