Forced expression of reprogramming factors can convert somatic cells into induced pluripotent stem cells (iPSCs). Here we studied genome topology dynamics during reprogramming of different somatic cell types with highly distinct genome conformations. We find large-scale topologically associated domain (TAD) repositioning and alterations of tissue-restricted genomic neighborhoods and chromatin loops, effectively erasing the somatic-cell-specific genome structures while establishing an embryonic stem-cell-like 3D genome. Yet, early passage iPSCs carry topological hallmarks that enable recognition of their cell of origin. These hallmarks are not remnants of somatic chromosome topologies. Instead, the distinguishing topological features are acquired during reprogramming, as we also find for cell-of-origin-dependent gene expression patterns.