Gene regulation is a process with many steps allowing for stochastic biochemical reactions, which leads to expression noise-i.e., the cell-to-cell stochastic fluctuation in protein abundance. Such expression noise can give rise to drastically diverse phenotypes, even within isogenic cell populations. Although numerous biophysical approaches had been proposed to model the origin and propagation of expression noise in biological networks, these models essentially characterize the innate stochastic dynamics in gene regulation in a mechanistic way. In this work, by investigating expression noise in the context of yeast cellular networks, we place the biophysical formulism onto solid genetic ground. At the sequence level, we show that extremely noisy genes are highly conserved in their coding sequences. At the level of cellular networks where natural selection is manifested by the topological constraints, we show that genes with varying expression noise are modularly organized in the protein interaction network and are positioned orderly in the gene regulatory network. We demonstrate that these topological constraints are highly predictive of stochastic gene expression, with which we were able to confidently predict stochastic expression for more than 2,000 yeast genes whose expression noise was previously not known. We validated the predictions by high-content cell imaging. Our approach makes feasible genome-wide prediction of stochastic gene expression, and such predictability in turn suggests that expression noise is an evolvable genetic trait.