But the Senate must also approve the package, and that vote won't happen before mid-July, despite a recent push by Democrats to send the bill to the president by July 4.
The reasons for the delay: the death of Sen. Robert Byrd (D) of West Virginia and questions about whether the Republicans who have provided crucial support for the reforms at earlier stages will still be counted as "yes" votes.
This week, Democrats sought to confirm the support of Sen. Scott Brown (R) of Massachusetts, who threatened to vote against the bill if it contained $19 billion in new fees on large banks and hedge funds. House and Senate conferees reconvened to remove that provision, but on Wednesday Senator Brown didn't commit his vote. He said he plans to evaluate the bill over Congress's week-long July 4 recess.
The House vote on Wednesday ran largely along party lines, coming in at 237 to 192.
Democrats hailed the measure as a vital step to safeguard Main Street from the risks and excesses of Wall Street and to prevent another financial crash like the one that walloped the economy in 2008. Republicans said the bill will perpetuate the problem of "too big to fail" banks, codifying the importance of large banks through new levels of regulation.
"[It] makes the bad ideas of the Wall Street bailout permanent," Rep. Mike Pence (R) of Indiana said before the House vote. He and other Republicans have argued that large banks should face the threat of failure in bankruptcy if they perform poorly, as an incentive for private-sector prudence.
The bill's proponents say it will reduce the risk of another financial catastrophe. The measure seeks to enhance regulatory supervision of financial firms, prod the biggest banks to hold more capital as a cushion in hard times, and set up a new mechanism for "orderly liquidation" of failing firms by the Federal Deposit Insurance Corp., without direct costs to taxpayers.
The bill would also set up a new consumer-protection agency for financial products such as mortgages.
Mr. Obama lashed out at Republican critics of the bill Wednesday in Wisconsin. He took House Republican leader John Boehner to task for saying the financial-reform bill is so extensive that it "is like killing an ant with a nuclear weapon."
"He can't be that out of touch with the struggles of American families," Obama said. "And if he is, he has to come here to Racine and ask people if they think the financial crisis was an ant."
The math in the Senate revolves around the need for a filibuster-proof 60 votes. Republicans hold 41 of the 100 seats, and two Democrats have voted against the bill. So several Republican votes are needed, along with the vote of whoever is tapped to fill the seat that belonged to Mr. Byrd.
• Wire service material was used in this report.