The researchers in Berlin said the man, who suffered from leukaemia and HIV, had shown no sign of either disease since the transplant two years ago.
But they stressed it was an unusual case which needed further investigation.
Experts said the result may boost interest in gene therapy for HIV.
Berlin's Charite clinic said the 42-year-old patient was an American living in Berlin, but the man has not been identified.
He had been infected with the human immunodeficiency virus, that causes Aids, for more than a decade and also had leukaemia.
The clinic said since the transplant was carried out 20 months ago, tests on the patient's bone marrow, blood and other organ tissues have all been clear.
In a statement, Professor Rodolf Tauber from the Charite clinic said: "This is an interesting case for research.
"But to promise to millions of people infected with HIV that there is hope of a cure would not be right."
Roughly one in 1,000 Europeans and Americans have an inherited genetic mutation, which prevents HIV from attaching itself to cells.
Two million people die of Aids every year and HIV is estimated to have infected 33 million people worldwide.
Option 'for a few'
Professor Andrew Sewell, from the Department of Medical Biochemistry and Immunology at the University of Cardiff said in theory a bone marrow transplant such as this one "should work" and it was surprising that no one had tried it before.
"The problem is most people with HIV live in sub-Saharan Africa and this is hugely expensive, you have to find a matched donor, and it's a pretty severe and painful operation.
"So it's going to be an option for very few people."
He added that gene therapy to knock out the mutation of the key CCR5 receptor was a possibility for future treatment.
Professor Philip Goulder, an immunologist at the University of Oxford said: "It's a really interesting case which looks at a treatment which really hasn't been thought about before.
"But without having that much information about the specific case you would want to be very cautious about getting too excited and you wouldn't be able to replicate that treatment for a lot of people with HIV."
Paul Ward, deputy chief executive at the Terrence Higgins Trust said: "This case gives us something to explore in future studies but it's certainly not a quick fix as gene therapy is complex and expensive.
"With no cure in sight, prevention should be our number one priority."