Gene expression levels can be subject to selection. We hypothesized that the age of gene origin is associated with expression constraints, given that it affects the level of gene integration into the functional cellular environment. By studying the genetic variation affecting gene expression levels (cis expression quantitative trait loci [cis-eQTLs]) and protein levels (cis protein QTLs [cis-pQTLs]), we determined that young, primate-specific genes are enriched in cis-eQTLs and cis-pQTLs. Compared to cis-eQTLs of old genes originating before the zebrafish divergence, cis-eQTLs of young genes have a higher effect size, are located closer to the transcription start site, are more significant, and tend to influence genes in multiple tissues and populations. These results suggest that the expression constraint of each gene increases throughout its lifespan. We also detected a positive correlation between expression constraints (approximated by cis-eQTL properties) and coding constraints (approximated by Ka/Ks) and observed that this correlation might be driven by gene age. To uncover factors associated with the increase in gene-age-related expression constraints, we demonstrated that gene connectivity, gene involvement in complex regulatory networks, gene haploinsufficiency, and the strength of posttranscriptional regulation increase with gene age. We also observed an increase in heritability of gene expression levels with age, implying a reduction of the environmental component. In summary, we show that gene age shapes key gene properties during evolution and is therefore an important component of genome function.