How do we perceive the fundamental distinction between the physical self and the external world, and how do we come to sense that an object in view, for example, a hand, is part of our own body or not? Over the past two decades, many studies have investigated the contributions of vision, touch, and proprioception to the sense of body ownership, i.e., the multisensory perception of limbs and body parts as our own. However, the processes involved in subjectively experienced body ownership have only been qualitatively described, and the computational principles that determine such sensations remain unclear. To address this issue, we developed a detection-like psychophysics task based on the classic rubber hand illusion paradigm where participants were asked to report whether the rubber hand felt like their own (the illusion) or not. We manipulated illusion strength by varying the asynchrony of visual and tactile stimuli delivered to the rubber hand and the hidden real hand under different levels of visual noise. We found that (1) the probability of the emergence of the rubber hand illusion increased with the addition of visual noise and was well predicted by a causal inference model involving the observer computing the probability of the visual and tactile signals coming from a common source; (2) the causal inference model outperformed a non-Bayesian model involving the observer not taking into account sensory uncertainty; and (3) by comparing the casual inference of ownership and visuotactile synchrony detection, we found that the prior probability of inferring a common cause for the two types of multisensory precepts was correlated but greater for ownership, which suggests that individual differences in rubber hand illusion can be explained at the computational level as differences in how priors are used in the multisensory integration process. Collectively, these results demonstrate that the sense of body ownership is determined by Bayesian causal inference, which implies that the same statistical principles determine the perception of the bodily self and the external world.