The move follows outrage over the decision by AIG to award its employees $165 million in bonuses after taking $170 billion in aid from the government.
House Speaker Nancy Pelosi said: "We want our money back and we want our money back now for the taxpayers."
President Barack Obama welcomed the result of the vote."Now this legislation moves to the Senate, and I look forward to receiving a final product that will serve as a strong signal to the executives who run these firms that such compensation will not be tolerated," Obama said.
Members of the house voted 328-93 in favor of the legislation. The bill targets companies that received $5 billion in taxpayer aid, and would levy a 90% tax on bonuses paid to employees with incomes above $250,000.
The bill was opposed by some Republicans, who argued that the legislation diverted attention from the administration's handling of the affair.
Some Republicans have called for US Treasury Secretary Timothy Geithner to step down.
In total, 243 Democrats and 85 Republicans voted in favor of the bill, which was passed with unusual speed. It was opposed by six Democrats and 87 Republicans.
"The whole idea that they should be rewarded millions of dollars is repugnant to everything that decent people believe in," said Charlie Rangel, the Democratic chairman of the Ways and Means Committee.
Mr. Geithner has been under pressure since news of the bonuses became public.He said that the government would deduct the bonuses from government funds due to be paid to the insurer.
President Barack Obama has also reiterated his anger at the bonus payments.
Edward Liddy, the boss of AIG, on Wednesday called the bonuses paid to executives "distasteful" and said he had asked some recipients to return at least half of what they had been paid.
"Mistakes were made at AIG on a scale that few could have imagined possible," he said.
But Mr. Liddy, who took over AIG in September, told a Congressional committee that the Federal Reserve knew in November of the bonus payments to executives. He said he spoke regularly with the Fed, expecting them to pass on the details to Treasury officials.
An investigation into AIG bonus payments was launched earlier on Thursday.
Neil Barofsky, the special inspector general, told Congress he would look specifically at the Treasury's role.
Mr. Barofsky said he would "act aggressively to recover the taxpayer's money" if there was any evidence that something wrong was done to approve the bonuses.