The circadian clock modulates human physiology. However, the organization of tissue-specific gene expression rhythms and how these depend on age and sex is not defined in humans. We combined data from the Genotype-Tissue Expression (GTEx) project with an algorithm that assigns circadian phases to 914 donors, by integrating temporal information from multiple tissues in each individual, to identify messenger RNA (mRNA) rhythms in 46 tissues. Clock transcripts showed conserved timing relationships and tight synchrony across the body. mRNA rhythms varied in breadth, covering global and tissue-specific functions, including metabolic pathways and systemic responses. The clock structure was conserved across sexes and age groups. However, overall gene expression rhythms were highly sex-dimorphic and more sustained in females. Rhythmic programs generally dampened with age across the body.