The House voted 359-68 in favour of the legislation on Wednesday, which must now be approved by the Senate before the president can sign it into law.
Amendments aimed at putting limits on India's nuclear weapons programme, that were proposed by those concerned that the deal would harm non-proliferation goals, were rejected.
Representatives also rejected an effort to delay action until India did more to back US efforts to contain Iran.
The deal - agreed with Manmohan Singh, the Indian prime minister, in March - would allow India to buy American nuclear reactors and fuel for the first time in more than 30 years, despite the fact it has still not signed the nuclear Non-Proliferation Treaty.
New Delhi will be required to open civilian nuclear facilities to inspections, give up future nuclear tests and work with the US and other nations on stopping the spread of nuclear exports.
Tom Lantos, the senior Democrat on the House International Relations Committee, said: "History will regard what we do today as a tidal shift in relations between India and the United States. This will be known as the day when Congress signalled definitively the end of the Cold War paradigm governing interactions between New Delhi and Washington."
The Senate is not expected to vote on the deal until September.
The House and Senate would have to vote again after US-India talks on the technical details of the agreement are completed.
India must also complete negotiations with the International Atomic Energy Agency on a system of inspections for its civilian nuclear facilities and the 45-nation Nuclear Suppliers Group must change its regulations to allow nuclear transfers to India.
Eight military nuclear sites would be off-limits to inspectors under the deal.
Edward Markey, head of a bipartisan non-proliferation task force, criticised the deal as pouring "nuclear fuel on the fire of an India-Pakistan nuclear arms race" because it would allow New Delhi to expand its nuclear weapons production from seven to more than 50 bombs a year.
Legislators warned India that its technology should only be used to meet the South Asian nation's growing energy demands, and co-operation would end if India tested another nuclear weapon, as it did in 1974 and 1998.