Medawar's mutation accumulation hypothesis explains aging by the declining force of natural selection with age: Slightly deleterious germline mutations expressed in old age can drift to fixation and thereby lead to aging-related phenotypes. Although widely cited, empirical evidence for this hypothesis has remained limited. Here, we test one of its predictions that genes relatively highly expressed in old adults should be under weaker purifying selection than genes relatively highly expressed in young adults. Combining 66 transcriptome datasets (including 16 tissues from five mammalian species) with sequence conservation estimates across mammals, here we report that the overall conservation level of expressed genes is lower at old age compared to young adulthood. This age-related decrease in transcriptome conservation (ADICT) is systematically observed in diverse mammalian tissues, including the brain, liver, lung, and artery, but not in others, most notably in the muscle and heart. Where observed, ADICT is driven partly by poorly conserved genes being up-regulated during aging. In general, the more often a gene is found up-regulated with age among tissues and species, the lower its evolutionary conservation. Poorly conserved and up-regulated genes have overlapping functional properties that include responses to age-associated tissue damage, such as apoptosis and inflammation. Meanwhile, these genes do not appear to be under positive selection. Hence, genes contributing to old age phenotypes are found to harbor an excess of slightly deleterious alleles, at least in certain tissues. This supports the notion that genetic drift shapes aging in multicellular organisms, consistent with Medawar's mutation accumulation hypothesis.