The use of mesenchymal stromal cells (MSCs) in regenerative medicine and tissue engineering is well established, given their properties of self-renewal and differentiation. However, several studies have shown that these properties diminish with age, and understanding the pathways involved are important to provide regenerative therapies in an ageing population. In this PRISMA systematic review, we investigated the effects of chronological donor ageing on the senescence of MSCs. We identified 3023 studies after searching four databases including PubMed, Web of Science, Cochrane, and Medline. Nine studies met the inclusion and exclusion criteria and were included in the final analyses. These studies showed an increase in the expression of p21, p53, p16, ROS, and NF-κB with chronological age. This implies an activated DNA damage response (DDR), as well as increased levels of stress and inflammation in the MSCs of older donors. Additionally, highlighting the effects of an activated DDR in cells from older donors, a decrease in the expression of proliferative markers including Ki67, MAPK pathway elements, and Wnt/β-catenin pathway elements was observed. Furthermore, we found an increase in the levels of SA-β-galactosidase, a specific marker of cellular senescence. Together, these findings support an association between chronological age and MSC senescence. The precise threshold for chronological age where the reported changes become significant is yet to be defined and should form the basis for further scientific investigations. The outcomes of this review should direct further investigations into reversing the biological effects of chronological age on the MSC senescence phenotype.