He had been living with a recurrence of leukaemia for several months and received hospice care at his home in Palm Springs, California.
"On behalf of all its members... the IAS sends its condolences to Timothy's partner, Tim, and his family and friends," said IAS President Adeeba Kamarulzaman.
"We owe Timothy and his doctor, Gero Hutter, a great deal of gratitude for opening the door for scientists to explore the concept that a cure for HIV is possible."
Brown was diagnosed with HIV while he was studying in Berlin in 1995. A decade later, he was diagnosed with leukaemia, a cancer that affects the blood and bone marrow.
To treat his leukaemia, his doctor at the Free University of Berlin used a stem cell transplant from a donor who had a rare genetic mutation that gave him natural resistance to HIV, hoping it may wipe out both diseases.
It took two painful and dangerous procedures, but it was a success: in 2008 Brown was declared free of the two ailments, and was initially dubbed "the Berlin Patient" at a medical conference to preserve his anonymity.
Two years later, he decided to break his silence and went on to become a public figure, giving speeches and interviews and starting his own foundation.
"I am living proof that there could be a cure for AIDS," he told AFP in 2012. "It's very wonderful, being cured of HIV."
Ten years after Brown was cured, a second HIV patient - dubbed "the London Patient" - was revealed to be in remission 19 months after undergoing a similar procedure.
The patient, Adam Castillejo, is currently HIV-free. In August a California woman was reported to have no traces of HIV despite not using anti-retroviral treatment.
It is thought she may be the first person to be cured of HIV without undergoing the risky bone marrow treatment.
Sharon Lewin, president-elect of the IAS and director of the Doherty Institute in Melbourne, Australia, praised Brown as a "champion and advocate" of a cure for HIV.
"It is the hope of the scientific community that one day we can honour his legacy with a safe, cost-effective and widely accessible strategy to achieve HIV remission and cures using gene editing or techniques that boost immune control," she said.