Demi-Lee Brennan was aged nine and seriously ill with liver failure when she received the transplant, doctors at a top Sydney children's hospital told AFP.
Nine months later they discovered she had changed blood types and that her immune system had switched over to that of the donor after stem cells from the new liver migrated to her bone marrow.
She is now a healthy 15-year-old, Michael Stormon, a hepatologist treating her, told AFP. He said he had given several presentations on the case around the world and had heard of none like it.
"It is extremely unusual -- in fact we don't know of any other instance in which this happened," Stormon told AFP from the Children's Hospital at Westmead.
"In effect she had had a bone marrow transplant. The majority of her immune system had also switched over to that of the donor."
An article on the case was published in Thursday's edition of the leading US medical journal The New England Journal of Medicine.
Brennan's mother Kerrie Mills described the recovery as "miraculous" while the patient herself told a news conference that doctors had given her life back to her.
"I just can't thank them enough. It's like my second chance at life," Brennan said.
Doctors who treated Brennan are interested to know if the case could have other applications in transplant surgery, where rejection of donor organs by the recipient's immune system is a major hurdle.
Stormon said it appeared that Brennan may have been fortunate because a "sequence of serendipitous events", including a post-transplantation infection, may have given the stem cells from her donor's liver the chance to proliferate in the bone marrow, where blood cells develop.
The task now was to establish whether the same sort of outcome could be replicated in other transplant patients, he said.
"The challenge for us now is to try and figure out how this occurred," Stormon said.
One possibility is that the series of events she experienced all weakened her immune system enough for the stem cells to migrate to the bone marrow and proliferate, Stormon said.
These factors include the particular type of liver failure she had, a post-operation infection with the virus cytomegalovirus, and immunosuppressive drugs.
"To try to replicate that is easier said than done," Stormon said, but added the case could still potentially be of crucial importance.
"The holy grail of transplant medicine is immuno-tolerance. She exemplifies that this can occur."