Living organisms are continuously challenged by changes in their environment that can propagate to stresses at the cellular level, such as rapid changes in osmolarity or oxygen tension. To survive these sudden changes, cells have developed stress-responsive mechanisms that tune cellular processes. The response of Saccharomyces cerevisiae to osmostress includes a massive reprogramming of gene expression. Identifying the inherent features of stress-responsive genes is of significant interest for understanding the basic principles underlying the rewiring of gene expression upon stress. Here, we generated a comprehensive catalog of osmostress-responsive genes from 5 independent RNA-seq experiments. We explored 30 features of yeast genes and found that 25 (83%) were distinct in osmostress-responsive genes. We then identified 13 non-redundant minimal osmostress gene traits and used statistical modeling to rank the most stress-predictive features. Intriguingly, the most relevant features of osmostress-responsive genes are the number of transcription factors targeting them and gene conservation. Using data on HeLa samples, we showed that the same features that define yeast osmostress-responsive genes can predict osmostress-responsive genes in humans, but with changes in the rank-ordering of feature-importance. Our study provides a holistic understanding of the basic principles of the regulation of stress-responsive gene expression across eukaryotes.