Bodily illusions have fascinated humankind for centuries, and researchers have studied them to learn about the perceptual and neural processes that underpin multisensory channels of bodily awareness. The influential rubber hand illusion (RHI) has been used to study changes in the sense of body ownership: how a limb is perceived to belong to one’s body, which is a fundamental building block in many theories of bodily awareness, self-consciousness, embodiment, and self-representation. However, the methods used to quantify perceptual changes in bodily illusions — including the RHI — have mainly relied on subjective questionnaires and rating scales, and the degree to which such illusory sensations depend on sensory information processing has been difficult to test directly. Here we introduce a signal detection theory (SDT) framework to study the sense of body ownership in the RHI. We provide evidence that the illusion is associated with changes in body ownership sensitivity that depend on the information carried in the degree of asynchrony of correlated visual and tactile signals, as well as perceptual bias and sensitivity that reflect the distance between the rubber hand and the participant’s real body. We found that the illusion’s sensitivity to asynchrony is remarkably precise; even a 50 ms visuo-tactile delay significantly affected body ownership sensitivity. Our findings conclusively link changes in a complex bodily experience such as body ownership to basic sensory information processing and provide a proof of concept that SDT can be used to study bodily illusions.