Circadian rhythms are endogenous ∼24-hour cycles that significantly influence physiological and behavioral processes. These rhythms are governed by a transcriptional-translational feedback loop of core circadian genes and are essential for maintaining overall health. The study of circadian rhythms has expanded into various omics datasets, necessitating accurate analytical methodology for circadian biomarker detection. Here, we introduce a novel Bayesian framework for the genome-wide detection of circadian rhythms that is capable of incorporating prior biological knowledge and adjusting for multiple testing issue via a false discovery rate approach. Our framework leverages a Bayesian hierarchical model and employs a reverse jump Markov chain Monte Carlo (rjMCMC) technique for model selection. Through extensive simulations, our method, BayesCircRhy, demonstrated superior false discovery rate control over competing methods, robustness against heavier-tailed error distributions, and better performance compared to existing approaches. The method's efficacy was further validated in two RNA-Sequencing data, including a human resitrcted feeding data and a mouse aging data, where it successfully identified known and novel circadian genes. R package "BayesianCircadian" for the method is publicly available on GitHub https://github.com/jxncdhc/BayesianCircadian .