On a visit to Asia, George Bush, the US president, hailed the passage of the deal saying it would bring India into the "non-proliferation mainstream".
India said it was pleased with the approval, but said more steps remained as the bill needs to be voted jointly by both houses of congress.
Bush and Manmohan Singh, the Indian prime minister, had agreed to the deal in July last year when Singh paid a visit to Washington. They reaffirmed it during the US leader's visit to New Delhi in March.
Controversial bill
The agreement was seen as controversial because the US congress had to create a rare exception for India from some of the requirements of the US Atomic Energy Act, which currently prohibits nuclear sales to non-NPT signatories.
In addition, US weapons experts said that forging such an agreement with non-NPT member India would not only make it harder to enforce rules against countries such as Iran and North Korea, but also set a dangerous precedent for other countries with nuclear programmes.
Richard Lugar, a Republican senator and co-author of the bill, said: "This agreement is the most important strategic diplomatic initiative undertaken by President Bush."
US officials say the Bush administration had won a commitment from New Delhi to negotiate a so-called Fissile Material Cutoff Treaty, as part of a multilateral approach to reduce nuclear tension surrounding any potential arms race in South Asia.
The US House of Representatives approved the nuclear deal in July, but a senate vote had been delayed due to the US midterm elections last week that resulted in Democratic party control of both chambers in the new congress from January.
The senate and the House are scheduled to meet next month to reconcile several amendments they had made and that need to be approved again by the two chambers before Bush signs the final bill into law.