A balance between gene expression stability and evolvability is essential for the long-term maintenance of a living system. We studied whether the genetic and epigenetic properties of the promoter affect gene expression variability. We tested the hypothesis that upstream distance and orientation (head-to-head or head-to-tail) are important for the promoter architecture and gene expression variability. We found that in budding yeast genes with a short upstream distance tend to have low gene expression variability, and their promoter is flanked by strongly positioned nucleosomes and tends to have low nucleosome occupancy. These observations suggest that in vivo positioning of the flanking nucleosomes facilitates stable nucleosome depletion at the core promoter region and enhances gene expression stability. Head-to-head genes have, on average, lower gene expression variability, greater nucleosome depletion at the core promoter region, and more strongly positioned nucleosomes that flank the core promoter than do head-to-tail genes. These observations hold for diverse eukaryotes, underscoring the importance of genome organization in balancing between robustness and evolvability of gene expression regulation.