The bill, passed by a vote of 308 to 116, also removes a current requirement, criticised by some Democrats and Aids activists, that a third of all HIV prevention funds be spent on sexual abstinence education.
It instead calls for "balanced funding" for abstinence, fidelity and condom programmes.
An estimated 33.2 million people around the world are said to be living with Aids with about 2.1 million deaths reported in 2007.
In 2006, about 9.2 million new cases of tuberculosis were detected against 9.1 million in 2005, the WHO said in its annual report on control of the disease earlier this month.
It is estimated that, including non-detected cases, there were 14.4 million cases of the disease worldwide in 2006.
The White House has called the anti-Aids initiative the largest commitment ever by any nation for an international health initiative dedicated to a single disease.
Opponents of the bill, however, said it was too expensive.
"It is terrible that millions of Africans are suffering Aids. But we cannot afford such totally irrational generosity. This is benevolence gone wild," Dana Rohrabacher, a Republican from California, said.
"We can't take care of our own veterans when they come home from the war. We can't take care of our elderly. We have people who can't take care of their own health needs and are at risk of losing their homes," Rohrabacher added.
"We have big hearts. But we need to use our brains."