Ex vivo, human mesenchymal stem cells (hMSCs) undergo spontaneous cellular senescence after a limited number of cell divisions. Intranuclear structures of the nuclear lamina were formed in senescent hMSCs, which are identified by the presence of Hayflick-senescence-associated factors. Notably, spatial changes in lamina shape were observed before the Hayflick senescence-associated factors, suggesting that the lamina morphology can be used as an early marker to identify senescent cells. Here, we applied quantitative image-processing tools to study the changes in nuclear architecture during cell senescence. We found that centromeres and telomeres colocalised with lamina intranuclear structures, which resulted in a preferred peripheral distribution in senescent cells. In addition, telomere aggregates were progressively formed during cell senescence. Once formed, telomere aggregates showed colocalization with gamma-H2AX but not with TERT, suggesting that telomere aggregates are sites of DNA damage. We also show that telomere aggregation is associated with lamina intranuclear structures, and increased telomere binding to lamina proteins is found in cells expressing lamina mutants that lead to increases in lamina intranuclear structures. Moreover, three-dimensional image processing revealed spatial overlap between telomere aggregates and lamina intranuclear structures. Altogether, our data suggest a mechanical link between changes in lamina spatial organization and the formation of telomere aggregates during senescence of hMSCs, which can possibly contribute to changes in nuclear activity during cell senescence.