Transcriptomic data yields valuable insights into cell type, tissue, and organ evolution. However, interpreting this data requires understanding how transcriptomes evolve. A particularly difficult problem is that cell type transcriptomes may not evolve independently. Here we present a statistical model to estimate the level of concerted transcriptome evolution and apply it to published and new data. The results indicate that tissues undergo pervasive concerted evolution in gene expression. Tissues related by morphology or developmental lineage exhibit higher levels of concerted evolution. Concerted evolution also causes tissues from the same species to be more similar in gene expression to each other than to homologous tissues in another species. This result may explain why some tissue transcriptomes cluster by species rather than homology. Our study illustrates the importance of accounting for concerted evolution when interpreting comparative transcriptome data, and should serve as a foundation for future investigations of cell type evolution.