The genetics of lifespan determination is poorly understood. Most research has been done on short-lived animals and it is unclear if these insights can be transferred to long-lived mammals like humans. Some African mole-rats (Bathyergidae) have life expectancies that are multiple times higher than similar sized and phylogenetically closely related rodents. To gain new insights into genetic mechanisms determining mammalian lifespans, we obtained genomic and transcriptomic data from 17 rodent species and scanned eleven evolutionary branches associated with the evolution of enhanced longevity for positively selected genes (PSGs). Indicating relevance for aging, the set of 250 identified PSGs showed in liver of long-lived naked mole-rats and short-lived rats an expression pattern that fits the antagonistic pleiotropy theory of aging. Moreover, we found the PSGs to be enriched for genes known to be related to aging. Among these enrichments were "cellular respiration" and "metal ion homeostasis", as well as functional terms associated with processes regulated by the mTOR pathway: translation, autophagy and inflammation. Remarkably, among PSGs are RHEB, a regulator of mTOR, and IGF1, both central components of aging-relevant pathways, as well as genes yet unknown to be aging-associated but representing convincing functional candidates, e.g. RHEBL1, AMHR2, PSMG1 and AGER. Exemplary protein homology modeling suggests functional consequences for amino acid changes under positive selection. Therefore, we conclude that our results provide a meaningful resource for follow-up studies to mechanistically link identified genes and amino acids under positive selection to aging and lifespan determination.