The London patient, who was being treated for cancer, has now been in remission from HIV for 18 months and is no longer taking HIV drugs.
The researchers say it is too early to say the patient is “cured” of HIV.
Experts say the approach is not practical for treating most people with HIV but may one day help find a cure.
The male London patient, who has not been named, was diagnosed with HIV in 2003 and advanced Hodgkin’s lymphoma in 2012.
He had chemotherapy to treat the Hodgkin’s cancer and, in addition, stem cells were implanted into the patient from a donor resistant to HIV, leading to both his cancer and HIV going into remission.
Researchers from University College London, Imperial College London, Cambridge and Oxford Universities were all involved in the case.
This is the second time a patient treated this way has ended up in remission from HIV.
Ten years ago, another patient in Berlin received a bone-marrow transplant from a donor with natural immunity to the virus.
Timothy Brown, said to be the first person to “beat” HIV/Aids, was given two transplants and total body irradiation (radiotherapy) for leukaemia – a much more aggressive treatment.
“By achieving remission in a second patient using a similar approach, we have shown that the Berlin patient was not an anomaly and that it really was the treatment approaches that eliminated HIV in these two people,” said lead study author Prof Ravindra Gupta, from UCL.