It contains several amendments related to "the subject of US responses in the event of a future Indian nuclear test".
India has argued that it has the sovereign right to conduct such a test, while Washington has said the deal would be off if tests were carried out.
In a statement shortly after the bill was passed, Bush hailed the deal saying it will strengthen the US-India "strategic partnership" as well as efforts to halt the spread of atomic weapons.
"This legislation will strengthen our global nuclear non-proliferation efforts, protect the environment, create jobs, and assist India in meeting its growing energy needs in a responsible manner."
Washington banned nuclear trade with India after it carried out its first nuclear test in 1974 and refused to sign the Nuclear Non-Proliferation Treaty (NPT).
Signed by Bush and Manmohan Singh, the Indian prime minister, in July 2005, the deal offers India access to Western technology and cheap atomic energy.
In return New Delhi must allow UN inspections of some of its nuclear facilities.
Critics fear the deal weakens any position taken on nuclear programmes in other countries, such as Iran.
"President Bush and his aides were so eager for a foreign policy success that they didn't even try to get India to limit its weapons programme in return," the New York Times said in an editorial on Tuesday.
"They got no promise from India to stop producing bomb-making material, no promise to to expand its arsenal, and no promise not to resume nuclear testing."
The reaction in New Delhi has been marked by relief and satisfaction.
Speaking to Al Jazeera on Thursday, Krishnaswami Subrahmanyam, an Indian defence analyst, said: "[The nuclear deal] will expedite India's economic growth because it will add to India's energy.
"So far, India has been denied dual-use technology under the energy guidelines, so these are the benefits that India would receive under the new agreements."
He said India cannot give up its weapons because it is situated between two countries which are nuclear weapon powers, China and Pakistan.
"The non-proliferation community did not stop such proliferation in the past and therefore India is compelled to have its [own] nuclear arsenal," Subrahmanyam said.
"While India's record on non-proliferation has been scrupulous, Pakistan cannot make the same claim. You have the whole story of Dr AQ Khan [a Pakistani nuclear scientist who sold nuclear secrets to other countries]. The major powers have decided that Pakistan has not earned the same treatment [as India]."