Recent studies have shown that human perception of body ownership is highly malleable. A well-known example is the rubber hand illusion (RHI) wherein ownership over a dummy hand is experienced, and is generally believed to require synchronized stroking of real and dummy hands. Our goal was to elucidate the computational principles governing this phenomenon. We adopted the Bayesian causal inference model of multisensory perception and applied it to visual, proprioceptive, and tactile stimuli. The model reproduced the RHI, predicted that it can occur without tactile stimulation, and that synchronous stroking would enhance it. Various measures of ownership across two experiments confirmed the predictions: a large percentage of individuals experienced the illusion in the absence of any tactile stimulation, and synchronous stroking strengthened the illusion. Altogether, these findings suggest that perception of body ownership is governed by Bayesian causal inference—i.e., the same rule that appears to govern the perception of outside world.