Adam Castillejo is still free of the virus more than 30 months after stopping antiretroviral therapy.
He was not cured by the HIV drugs, however, but by a stem-cell treatment, he received for cancer he also had, the Lancet HIV journal reports.
The donors of those stem cells have an uncommon gene that gives them, and now Mr. Castillejo, protection against HIV.
In 2011, Timothy Brown, the "Berlin Patient" became the first person reported as cured of HIV, three and half years after having similar treatment.
What is the treatment?
Stem-cell transplants appear to stop the virus being able to replicate inside the body by replacing the patient’s own immune cells with donor ones that resist HIV infection.
Adam Castillejo - the now 40-year-old "London Patient" who has decided to go public with his identity - has no detectable active HIV infection in his blood, semen or tissues, his doctors say.
It is now a year after they first announced he was clear of the virus and he still remains free of HIV.
Lead researcher Prof Ravindra Kumar Gupta, from the University of Cambridge, told BBC News: "This represents HIV cure with almost certainty.
"We have now had two and a half years with anti-retroviral-free remission.
"Our findings show that the success of stem-cell transplantation as a cure for HIV, first reported nine years ago in the Berlin Patient, can be replicated."
But it will not be a treatment for the millions of people around the world living with HIV.
The aggressive therapy was primarily used to treat the patients’ cancers, not their HIV.
And current HIV drugs remain very effective, meaning people with the virus can live long and healthy lives.
Prof Gupta said: "It is important to note that this curative treatment is high-risk and only used as a last resort for patients with HIV who also have life-threatening hematological malignancies.
"Therefore, this is not a treatment that would be offered widely to patients with HIV who are on successful antiretroviral treatment."
But it might offer hope of finding a cure, in the future, using gene therapy.