The causal role of aneuploidy in cancer initiation remains under debate since mutations of euploidy-controlling genes reduce cell fitness but aneuploidy strongly associates with human cancers. Telomerase activation allows immortal growth by stabilizing telomere length, but its role in aneuploidy survival has not been characterized. Here, we analyze the response of primary human cells and murine hematopoietic stem cells (HSCs) to aneuploidy induction and the role of telomeres and the telomerase in this process. The study shows that aneuploidy induces replication stress at telomeres leading to telomeric DNA damage and p53 activation. This results in p53/Rb-dependent, premature senescence of human fibroblast, and in the depletion of hematopoietic cells in telomerase-deficient mice. Endogenous telomerase expression in HSCs and enforced expression of telomerase in human fibroblasts are sufficient to abrogate aneuploidy-induced replication stress at telomeres and the consequent induction of premature senescence and hematopoietic cell depletion. Together, these results identify telomerase as an aneuploidy survival factor in mammalian cells based on its capacity to alleviate telomere replication stress in response to aneuploidy induction.