Congress approved a package earlier this month which lifted funding for the five-year program from 15 billion dollars, set in 2003, to the 48 billion dollars signed into law by Bush.
The US president had called during a trip to Africa in February for Congress to double funding for the program to 30 billion dollars, but the final sum was much larger.
The White House said the legislation -- the President's Emergency Plan for AIDS Relief (PEPFAR) -- was "the largest commitment by any nation to combat a single disease in human history."
"When the president launched this initiative in 2003, about 50,000 people in all of sub-Saharan Africa were receiving anti-retroviral treatment," the White House said in a statement.
"Today, PEPFAR supports lifesaving anti-retroviral treatment for nearly 1.7 million people in the region - and tens of thousands more around the world, from Asia to eastern Europe," it said.
The new program drops a requirement for one-third of the anti-AIDS funds to be used to promote sexual abstinence and lifts a ban on HIV-positive foreigners entering the United States.
Eric Friedman, the senior global health policy advisor for Physicians for Human Rights (PHR), praised the bill for lifting the travel ban on HIV-positive visitors, saying it had "been an embarrassment to this country for many years".
Gay rights group, Human Rights Campaign, also hailed the repeal of the US-entry ban on HIV-positive visitors and immigrants, which has stood since 1987.
"We appreciate the president signing the repeal of this unjust and sweeping policy that deems HIV-positive individuals inadmissible to the United States," said Human Rights Campaign president Joe Solmonese.
"The HIV travel and immigration ban performs no public health service, is unnecessary and ineffective," he added.
The legislation was "the boldest act of any wealthy nation in ameliorating Africa's disastrous health worker shortage" by providing funds to create 140,000 jobs in the sector, PHR's Friedman said.
But he criticised the program for not linking HIV services with family planning.
"That allows HIV to go unprevented and undetected for years, until a whole family is infected," he said.
Democratic Speaker of the House of Representatives, Nancy Pelosi, has praised the bill for taking the global fight against AIDS, tuberculosis and malaria "from the emergency phase to the sustainability phase."
The new legislation "is our compact with developing nations across the globe," Pelosi said in a statement last week, when Congress voted to increase funding for the program.
"It says that America stands with them in this fight, that our commitment will not waver, and shows them America's true face of compassion," she said.
About two thirds of the world's HIV-positive cases are in sub-Saharan Africa. At least one person in 10 lives with HIV in nations such as South Africa, Zimbabwe, Botswana, Lesotho, Malawi, Mozambique, Namibia, Swaziland and Zambia, the International Federation of the Red Cross and Red Crescent Societies (IFRC) said in a report published in June.
Malaria, meanwhile, kills more than a million people each year, 90 percent of them in sub-Saharan Africa, according to the World Health Organisation (WHO).
Deaths due to the mosquito-born disease sap more than a full percentage point from the annual economic growth of the most affected nations.
In a report issued in March, the WHO estimated that there were 14.4 million cases of tuberculosis (TB) worldwide in 2006.
That report drew attention to the significant number of HIV-infected people with TB. In 2006, some 700,000 new cases of HIV-infected people with TB were detected.