Simple multisensory manipulations can induce the illusory misattribution of external objects to one's own body, allowing to experimentally investigate body ownership. In this context, body ownership has been conceptualized as the result of the online Bayesian optimal estimation of the probability that one object belongs to the body from the congruence of multisensory inputs. This idea has been highly influential, as it provided a quantitative basis to bottom-up accounts of self-consciousness. However, empirical evidence fully supporting this view is scarce, as the optimality of the putative inference process has not been assessed rigorously. This pre-registered study aimed at filling this gap by testing a Bayesian model of hand ownership based on spatial and temporal visuo-proprioceptive congruences. Model predictions were compared to data from a virtual-reality reaching task, whereby reaching errors induced by a spatio-temporally mismatching virtual hand have been used as an implicit proxy of hand ownership. To rigorously test optimality, we compared the Bayesian model versus alternative non-Bayesian models of multisensory integration, and independently assess unisensory components and compare them to model estimates. We found that individually measured values of proprioceptive precision correlated with those fitted from our reaching task, providing compelling evidence that the underlying visuo-proprioceptive integration process approximates Bayesian optimality. Furthermore, reaching errors correlated with explicit ownership ratings at the single individual and trial level. Taken together, these results provide novel evidence that body ownership, a key component of self-consciousness, can be truly described as the bottom-up, behaviourally optimal processing of multisensory inputs.