Phenotypic variation among individuals plays a key role in evolution, since variation provides the material on which natural selection can act. One important link between genetic and phenotypic variation is gene expression. As for other phenotypes, the range of accessible expression variation is limited and biased by different evolutionary and developmental constraints. Gene expression variability broadly refers to the tendency of a gene to vary in expression (i.e., between individuals or cells) due to stochastic fluctuations or differences in genetic, epigenetic, or environmental factors, separately from the differences between conditions (e.g. organs), and is often estimated based on observed expression variance. The variance due to biomolecular stochasticity (transcriptional 'noise') and cell-to-cell heterogeneity has been well-studied in isogenic populations of unicellular organisms such as bacteria and yeasts. However, for more complex organisms with multiple cells, tissues, and organs sharing the same genetic background, the interplay between inter-individual expression variability, gene and organ function, and gene regulation remains an open question. In this study, we used highly multiplexed 3'-end Bulk RNA Barcoding and sequencing (BRB-seq) to generate transcriptome profiles spanning at least nine organs in outbred individuals of three ray-finned fish species: zebrafish, Northern pike, and spotted gar. For each condition, we measured the expression variance per gene independent of mean expression level as an estimate of its variability. We observed that lowly variable genes are enriched in cellular housekeeping functions whereas highly variable genes are enriched in stimulus-response functions. Furthermore, genes with highly variable expression between individuals evolve under weaker purifying selection at the coding sequence level, indicating that intra-species gene expression variability predicts inter-species protein sequence divergence. Genes that are broadly expressed across organs tend to be both highly expressed and lowly variable between individuals, whereas organ-biased genes are typically highly variable within their top organ of expression. For genes with organ-biased expression profiles, we inferred differences in selective pressure on gene regulation depending on their top organ. We found that genes with peak expression in the brain have low inter-individual expression variability across non-nervous organs, suggesting stabilizing selection on regulatory evolution of brain-biased genes. Conversely, liver-biased genes have highly variable expression across organs, implying weaker regulatory constraints. These patterns show that gene regulatory mechanisms evolved differently based on constraints on the primary organ.