Peripersonal space (PPS) is known as the representation of the area around the body. Past research has shown that inducing a full-body illusion (FBI) can lead to PPS extending at the physical body location. However, it is unclear whether such illusions may also result in PPS transferring to a virtual body that is separate from the physical body. Furthermore, whether this effect may change over the course of natural aging is currently unknown. In three experiments, we investigated whether inducing an FBI using an avatar presented from a third-person perspective in virtual reality, results in PPS transferring to the avatar, and whether this effect differs between young (YAs; 18–29 years) and older adults (OAs; 65–83 years). We utilized a manipulation involving either synchronous or asynchronous stroking for FBI induction and assessed ratings of avatar ownership as a subjective indicator of embodiment. Meanwhile effects on PPS were measured by differences in multisensory facilitation within a visuo-tactile task. While we found significantly stronger ownership ratings for synchronous compared to asynchronous stroking in both YAs and OAs, this difference, as well as the degree of ownership, was significantly weaker for OAs. Moreover, while a distance-dependent modulation of multisensory facilitation reflecting PPS at the avatar’s location was observed in two samples of YAs, this effect was absent in OAs. These findings suggest that PPS in YAs can transfer to an avatar in virtual reality, while age-related differences in susceptibility to the FBI might contribute to a lack of this effect in OAs.