"The three laureates have discovered two new viruses of great importance and the result of that has led to an improved global health," Jan Andersson, a member of the Nobel assembly at Sweden's Karolinska Institute, said.
Montagnier said that the award sent a strong message.
"It comes at a time when much progress has been done in research, but not enough because the epidemic is still there," Montagnier said.
"We are in Africa. Many infected people do not have access to medicine."
The award is a decisive vote for Montagnier in a long-running dispute over who discovered and identified the virus, Montagnier or Robert Gallo, then with the US National Cancer Institute.
Montagnier and Gallo each accused the other of working with contaminated samples and it took presidential-level negotiations to persuade the National Institutes of Health and the Institut Pasteur to share royalties for the discovery.
"There was no doubt as to who made the fundamental discoveries," Maria Masucci, a Nobel Assembly member, said.
Barre-Sinoussi said that the dispute with Gallo belonged in the past.
"It is a conflict to be forgotten. It is also true that American teams were important in the discovery of the virus, and that should be recognised," she said.
When Montagnier and Barre-Sinoussi began their research in the early 1980s, a hitherto undocumented immune deficiency syndrome had just begun infecting victims in the West.
The researchers found the virus killed immune cells called lymphocytes from both diseased and healthy donors.
Their findings helped explain how HIV damaged the immune system and made possible drugs that can now keep patients healthy.
"Isolation of the virus itself is going to be the single most important discovery that will allow us to develop a vaccine, if a vaccine is ever developed," said Adriano Boasso, an immunologist and Aids researcher at Imperial College in London.
Zur Hausen was recognised for research based on his idea that human papilloma virus, or HPV, caused cervical cancer, the second most common cancer among women.
The German scientist, who began his research in the 1970s, searched for different HPV types, detecting them in cervical cancer biopsies.
Harald zur Hausen is a German professor [AFP]
The virus types he identified are found in about 70 per cent of cervical tumours around the world.
An estimated 500,000 women are diagnosed with the disease year and about 300,000 die from it, mostly in the developing world, though vaccines today exist to combat it.
"HPV vaccination is increasingly recognised as an important public-health tool in tandem with cervical screening," said Nicholas Kitchin, the United Kingdom medical director at Sanofi Pasteur MSD.
Medicine is traditionally the first of the Nobel prizes awarded each year.
The prizes for achievement in science, literature and peace were first awarded in 1901 in accordance with the will of inventor Alfred Nobel.
The Nobel laureate for physics will be announced on Tuesday, chemistry on Wednesday, literature on Thursday and the Nobel Peace Prize on Friday in Oslo.