The study of the ubiquitous circadian rhythms in human physiology typically requires regular measurements across time. Repeated sampling of the different internal tissues that house circadian clocks is both practically and ethically infeasible. Here, we present a novel unsupervised machine learning approach (COFE) that can use single high-throughput (omics) samples from individuals to reconstruct circadian rhythms across cohorts. COFE can both assign time-labels to samples, and identify rhythmic data features used for temporal reconstruction. With COFE, we discovered widespread de novo circadian gene expression rhythms in eleven different human adenocarcinomas using data from the TCGA database. The arrangement of peak times of core clock gene expression was conserved across the cancers and resembled a healthy functional clock except for the mistiming of few key genes. The commonly rhythmic genes were involved in metabolism and the cell cycle. Although these rhythms were synchronized with the cell cycle in many cancers, they were uncoupled with clocks in healthy matched tissue. Moreover, rhythms in the transcriptome were strongly associated with the cancer-relevant proteome. The targets of most of FDA-approved and potential anti-cancer drugs were rhythmic in tumor tissue with different amplitudes and peak times, emphasizing the utility of considering "time" in cancer therapy. Our approach thus creates new opportunities to repurpose data without time-labels to study circadian rhythms.