Processes like cellular senescence are characterized by complex events giving rise to heterogeneous cell populations. However, the early molecular events driving this cascade remain elusive. We hypothesized that senescence entry is triggered by an early disruption of the cells' three-dimensional (3D) genome organization. To test this, we combined Hi-C, single-cell and population transcriptomics, imaging, and in silico modeling of three distinct cells types entering senescence. Genes involved in DNA conformation maintenance are suppressed upon senescence entry across all cell types. We show that nuclear depletion of the abundant HMGB2 protein occurs early on the path to senescence and coincides with the dramatic spatial clustering of CTCF. Knocking down HMGB2 suffices for senescence-induced CTCF clustering and for loop reshuffling, while ectopically expressing HMGB2 rescues these effects. Our data suggest that HMGB2-mediated genomic reorganization constitutes a primer for the ensuing senescent program.