The House voted 257-167 in a late-night session less than 24 hours after the Senate approved it by a vote of 89 to 8.
Only 85 of the 242 Republicans voted for it, but they did not push for an amendment to retain some immediate spending cuts which would have sent the bill back to Senate for another round of approval.
President Barack Obama, who interrupted his holiday in Hawaii for the New Year's Day session, said he would sign the compromise bill into law but warned the battle against the deficit would continue.
"The fact is the deficit is still too high, and we're still investing too little in the things that we need for the economy to grow as fast as it should," he said. "We can't simply cut our way to prosperity.
The agreement allows tax cuts implemented under former president George W Bush to expire for individuals earning more than 400,000 dollars a year and families earning more than 450,000 dollars.//DPA