Congressman Tom Lantos said the proposal, which reverses decades of U.S. anti-proliferation policy, is "a tidal shift in relations between India and the United States."
"We are at a hinge of history, as we seek to build a fundamentally new relationship," said Lantos, the top Democrat on the House International Relations Committee and a strong champion of the plan.
Wednesday's vote was 359 to 68.
The Senate has yet to vote on the plan, which must clear several more hurdles before nuclear trade between the two countries could begin.
For Bush to implement his accord with India, lawmakers must first exempt New Delhi from U.S. laws that bar nuclear trade with countries that have not submitted to full international inspections.
Congressional action is needed because India built its nuclear weapons program outside the Nuclear Non-Proliferation Treaty, which provides civil nuclear trade in exchange for a pledge from nations not to pursue nuclear weapons.
Before the vote, lawmakers made last-ditch attempts to attach conditions they said were needed to make sure the United States was not supporting a massive increase in India's nuclear stockpile. Powerful supporters of the accord quashed proposals they said would cause India to balk and the delicately worded deal to collapse.
Several lawmakers strongly questioned the initiative, arguing that it would undermine the world's premier nonproliferation treaty.
Democratic Congressman Ed Markey portrayed the plan as a "historic failure" that "pours nuclear fuel on the fire of an India-Pakistan nuclear arms race." Pakistan is India's nuclear-armed archrival and neighbor; Islamabad has not been offered a similar deal by the United States.
Bush and Indian Prime Minister Manmohan Singh agreed in March to a plan that would allow civil nuclear trade with India in return for safeguards and inspections at India's 14 civilian nuclear plants; eight military plants would be off-limits.
Supporters said the deal strengthens a strategic relationship with a friendly country that has long maintained a responsible nuclear program. It would also, they said, provide clean energy to a country desperate to fuel a booming economy.
Congressman Dennis Kucinich, a Democrat, disagreed, saying that "at this time of great crisis in the world, we should be looking for nuclear disarmament, nuclear abolition — saving the world, not ramping up for Armageddon by nuclear proliferation."
"We're going in the wrong direction here," he said.
While the initiative enjoys broad support from lawmakers in both political parties, several more steps remain.
The Nuclear Suppliers Group, an assembly of nations that export nuclear material, must decide whether to make an exception for India. Officials from India and the U.N. nuclear watchdog must also negotiate a safeguard agreement.
Once technical negotiations on an overall cooperation agreement are settled between India and the United States, the Congress would then stage another, expedited vote.