Friday's 354-67 vote sends the bill to the Senate, which expects to pass the bill later in the day. All of the no votes were cast by Republicans.
The bill gives more borrowing authority to the National Flood Insurance Program to pay about 115,000 pending claims.
Northeast lawmakers say the money is urgently needed for victims of one of the worst storms ever to strike the region. Boehner set Friday's vote after sparking controversy with a decision to delay House action on a broader Sandy aid package.