Ageing-relevant processes, like cellular senescence, are characterized by complex, often stochastic, events giving rise to heterogeneous cell populations. We hypothesized that entry into senescence of different primary human cells can be triggered by one early molecular event affecting the spatial organization of chromosomes. To test this, we combined whole-genome chromosome conformation capture, population and single-cell transcriptomics, super-resolution imaging, and functional analyses applied on proliferating and replicatively-senescent populations from three distinct human cell types.We found a number of genes involved in DNA conformation maintenance being suppressed upon senescence across cell types. Of these, the abundant high mobility group (HMG) B1 and B2 nuclear factors are quantitatively removed from cell nuclei before typical senescence markers appear, and mark a subset of topologically-associating domain (TAD) boundaries. Their loss coincides with obvious reorganization of chromatin interactions via the dramatic spatial clustering of CTCF foci.HMGB2 knock-down recapitulates this senescence-induced CTCF clustering, while also affecting insulation at TAD boundaries. We accordingly propose that HMGB-mediated deregulation of chromosome conformation constitutes a primer for the ensuing senescent program across cell types.