Compressive sensing (CS) allows acquiring sparse signals at sub-Nyquist rate, offering an energy-efficient solution to data acquisition. This is especially important to reduce communication data for mobile medical applications. However, reconstructing the signal from CS is usually left off-line due to the complex computations. In this paper, we integrate two key technologies to enable on-line energy-efficient CS signal reconstruction. These are (1) the use of Bayesian CS Belief Propagation (CS-BP) as the algorithm basis and (2) the novel design of stochastic computing (SC) circuits to efficiently map CS-BP algorithm. The overall signal reconstruction system is implemented with digital SC circuits in 65nm CMOS and recovers compressively sensed electrocardiography (ECG) and electromyography (EMG) signals with 11X to 8X data compression factor. Compared to a conventional binary design, post-layout simulation results show that the proposed stochastic design performs reconstruction with 5X energy-delay product improvement and 2X area reduction.