The bill retains a Senate ban on co-operation with India in areas of enrichment, reprocessing and heavy water production.
American and Indian officials will also need to work out a separate technical nuclear co-operation agreement, which is expected to be finalised next year.
As well as tackling India's energy shortages, the deal is expected to open up a market with an estimated value of up to $100bn to US companies.
The deal constitutes the first endorsement by any country of India’s nuclear status and its weapons programme.
Indian officials has said they have concerns over some of the bill's provisions.
The Indian foreign ministry said the US legislation contains "certain extraneous and prescriptive provisions" and pointed to language in the bill that would require George Bush, the US president, and his successors to determine if New Delhi is co-operating with US efforts to confront Iran over its nuclear programme.
A new provision requires the president to report annually to Congress on India's performance, but the deal would not be ended in the event of India failing to meet US expectations.
India's foreign ministry said in a statement: "No legislation enacted in a foreign country can take away from us the sovereign right to conduct foreign policy determined solely by our national interests."
India also has concerns about provisions that could limit its right to reprocess spent atomic fuel and employ other sensitive nuclear technologies.
MR Srinivasan, a member of the Indian government's Atomic Energy Commission, said: "We already possess these technologies.
"We have had the ability to reprocess since 1965 so this kind of language is causing us some concern."
He said there was also "the question of a future weapons test".
India conducted its first test of what it called a "peaceful nuclear device" on May 18, 1974.
Experts say India has already produced around 50 nuclear weapons.
Many argue selling India fuel for civilian energy use will free up New Delhi's indigenous uranium stocks for weapons. But further testing could nullify the deal with the US.
Srinivasan said: "There could be a legitimate reaction in an Indian test. Suppose Pakistan were to test."
Pakistan and India both have nuclear weapons and have fought three wars since 1947.
Talat Masood, a Pakistani defence analyst, said the US-India nuclear deal would bring about a "qualitative change in relations".
He said: "It will make Pakistan much more insecure."
Safeguards and inspections US law bars nuclear trade with India but Congressional approval of the bill creates an exemption that will allow US civilian nuclear trade with India, in exchange for Indian safeguards and inspections at its 14 civilian nuclear plants.
Eight military plants would remain off-limits.
"There could be a legitimate reaction in an Indian [nuclear] test. Suppose Pakistan were to test."
MR Srinivasan, member of the Indian government's Atomic Energy Commission
India has never signed the international nuclear nonproliferation treaty and has never submitted to full international inspections.
As lead signatory of the treaty, the US has been obligated to forswear assistance to the nuclear programmes of states that did not sign the treaty.
A multi-million dollar lobbying campaign by India and the US Chamber of Commerce was largely successful in preventing Congress from adding non-proliferation requirements that New Delhi found too burdensome.
Analysts are concerned that the US-India deal could start a nuclear arms race in South Asia.
Edward Markey, a Democrat Representative, called the deal a "historic mistake which will come back to haunt the United States and the world".
He said: "The United States expects the rest of the world to listen to us [on Iran], while we selectively grant exceptions to countries that never signed up to the nonproliferation treaty."