The 66-year-old has stopped taking HIV medication and says he is "beyond grateful" the virus can no longer be found in his body.
He was given a bone marrow transplant to treat blood cancer leukaemia from a donor who was naturally resistant.
The man, who does not want to be identified, is known as the "City of Hope" patient in honour of the hospital where he was treated in Duarte, California.
The sense of relief was clear as he opened up about many of his friends dying from HIV in the era before antiretroviral drugs could give people a near-normal life expectancy.
HIV was considered a 'death sentence' in the 1980s
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In a statement, the patient said: "When I was diagnosed with HIV in 1988, like many others, I thought it was a death sentence.
"I never thought I would live to see the day that I no longer have HIV."
The cure came as somewhat of a fluke, though.
The "City of Hope" patient had developed leukaemia at the age of 63 and his medical team decided he needed a bone marrow transplant to replace his cancerous blood cells.
By chance, the donor was resistant to HIV.
HIV gets into the body's white blood cells using a protein called CCR5, described as a doorway by scientists.
Some people, including the donor, have CCR5 mutations that close off the "door" and keep HIV out.
The "City of Hope" patient has now been in remission for more than 17 months.
A model of the HIV virus
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Dr Jana Dickter said: "We were thrilled to let him know that his HIV is in remission and he no longer needs to take antiretroviral therapy that he had been on for over 30 years."
The first patient in the world to be cured of HIV – the Berlin patient – was Timothy Ray Brown,
There have been three similar cases in the last three years.
Of all those cured, the "City of Hope" patient had lived with HIV for the longest time.
Dr Dickter told the BBC: "It's a complex procedure with significant potential side effects. So, it's not really a suitable option for most people living with HIV."
Prof Sharon Lewin, president-elect of the International AIDS Society, said: "A cure remains the Holy Grail of HIV research."