Peripersonal space (PPS), the interface between the self and the environment, is represented by a network of multisensory neurons with visual (or auditory) receptive fields anchored to specific body parts, and tactile receptive fields covering the same body parts. Neurophysiological and behavioural features of hand PPS representation have been previously modelled through a neural network constituted by one multisensory population integrating tactile inputs with visual/auditory external stimuli. Reference frame transformations were not explicitly modelled, as stimuli were encoded in pre-computed hand-centred coordinates. Here we present a novel model, aiming to overcome this limitation by including a proprioceptive population encoding hand position. We confirmed behaviourally the plausibility of the proposed architecture, showing that visuo-proprioceptive information is integrated to enhance tactile processing on the hand. Moreover, the network's connectivity was spontaneously tuned through a Hebbian-like mechanism, under two minimal assumptions. First, the plasticity rule was designed to learn the statistical regularities of visual, proprioceptive and tactile inputs. Second, such statistical regularities were simply those imposed by the body structure. The network learned to integrate proprioceptive and visual stimuli, and to compute their hand-centred coordinates to predict tactile stimulation. Through the same mechanism, the network reproduced behavioural correlates of manipulations implicated in subjective body ownership: the invisible and the rubber hand illusion. We thus propose that PPS representation and body ownership may emerge through a unified neurocomputational process; the integration of multisensory information consistently with a model of the body in the environment, learned from the natural statistics of sensory inputs.