HIV infects the immune system's T- lymphocytes
The scientists who discovered HIV will share the Nobel prize for medicine with the expert who linked human papilloma virus (HPV) to cervical cancer.
French team Françoise Barré-Sinoussi and Luc Montagnier were recognised for their groundbreaking work in uncovering the virus responsible for Aids.
Harald zur Hausen, from Germany, received the prize for making the link between HPV and cervical cancer.
More than 25 million people have died of HIV/Aids since 1981.
Globally, more than 33 million people are living with HIV.
Following medical reports of a new immunodeficiency syndrome in 1981, Professor Barre-Sinoussi, of the Institut Pasteur, and Dr Montagnier, director of the World Foundation for AIDS Research and Prevention, were the first to identify HIV as the culprit.
In its citation, the Nobel Assembly said their discovery was vital in enabling scientists to begin to understand the biology of a virus which continued to pose a huge public health threat throughout the globe.
Their work led to the development of methods to diagnose infected patients and to screen blood products, which has limited the spread of the pandemic.
It has also led to new treatments.
There is still no cure for HIV. However, for many the disease is no longer an imminent death sentence thanks to the major advances in research and drug development over recent years.
With treatment, people with HIV can live for decades with the condition.
However, HIV medicines are not widely available in many poor countries around the world.
The citation said: "Never before have science and medicine been so quick to discover, identify the origin and provide treatment for a new disease entity.
"Successful anti-retroviral therapy results in life expectancies for persons with HIV infection now reaching levels similar to those of uninfected people."
Nick Partridge of the HIV charity Terrence Higgins Trust said: "Françoise Barré-Sinoussi and Luc Montagnier are very deserving winners of the Noble Prize for Medicine.
"Their work was hugely significant, leading to enormous progress in the understanding and treatment of HIV."
Both Dr Montagnier and a US researcher Dr Robert Gallo are co-credited with discovering that HIV causes Aids, although for several years they staked rival claims that led to a legal and even diplomatic dispute between France and America.
The Nobel jury made no mention of Dr Gallo in its citation.
Professor Barré-Sinoussi said the award was "a great honour that I wasn't expecting."
Professor zur Hausen, of the University of Duesseldorf, was praised by the Nobel committee for going "against current dogma" to discover that HPV infection caused cervical cancer.
HPV can be detected in 99.7% of all women with cervical cancer, and persistent infection with the virus is estimated to be responsible for more than 5% of all cancers worldwide.
Professor zur Hausen's work helped others to develop vaccines against HPV, which are now routinely given to millions of teenage girls in many countries to prevent cervical cancer.
Dr Adriano Boasso, research fellow at Imperial College and Wellcome Trust Research Career Development Fellow, said: "Isolating the causing agent of an infectious disease is the single most important step toward developing a vaccine.
"The availability of a vaccine against HPV is now a reality thanks to the original discovery of the virus by Harald zur Hausen.
"HIV vaccine research has instead recently suffered the failure of promising clinical trials, but there is no doubt that the discovery of HIV by Françoise Barré-Sinoussi and Luc Montagnier will be the pillar on which an efficient vaccine will eventually be built."
Professor zur Hausen, 72, received half of the prize with Professor Barré-Sinoussi, 61, and Dr Montagnier, 76, splitting the other half.