In the rubber hand illusion (RHI), the feeling that a fake hand belongs to oneself can be induced by the simultaneous, congruent touch of the fake visible hand and one's own hidden hand. This condition is also associated with a recalibration of the perceived location of the real hand. A cortical network, including premotor and temporo-parietal areas, has been proposed as the basis of the RHI. However, the causal contribution of these areas to the discrete illusory components remains unclear. We used transcranial direct current stimulation (tDCS) to assess the contribution of the right premotor cortex (rPMc) and the right temporo-parietal junction (rTPJ) to the RHI and explored the role of these areas in modulating the subjective experience of embodiment and the misperception of the hand position. We found that anodal tDCS of both rPMc and rTPJ increased the misjudgement of the real hand location towards the fake hand. Crucially, the difference in proprioceptive displacement evoked by the congruent and incongruent visuo-tactile stroking was minimised when tDCS was applied over the rPMc, while it was amplified when the rTPJ was targeted. The parietal effects of tDCS also extended to the self-report components of the RHI. These findings suggest that the tDCS of rTPJ modulates the RHI depending on the temporal congruency of the visuo-tactile stimulation, while the tDCS of rPMc induces a general recalibration of hand coordinates, regardless of the visuo-tactile congruency. The present results are discussed in the view of a multicomponent model of the RHI.