The Senate's unanimous vote on Thursday came shortly after the House of Representatives passed an identical bill. The measure now goes to President George Bush for enactment.
Congress last week approved an initial $10.5 billion emergency package.
But with estimates of the costs of Katrina now approaching $200 billion, Republicans and Democrats in the House of Representatives expressed reservations about the runaway spending, and called for the appointment of an official to oversee and manage Katrina-related federal aid.
"When this much money gets put out this fast, there's a real danger … that we don't need to be too careful," said Republican Jeff Sessions on the floor of the Senate.
"Now we're seeing figures that it's going to be $200 billion to do this reconstruction, and we know - all of us know - that there's no money to pay for this," said Sessions, whose home state of Alabama, along with Mississippi and Louisiana, was devastated by Katrina.
No money left
Sessions pointed out that the US already is staggering under a massive budget deficit, believed to be about $331 billion, according to the most recent Congressional Budget Office estimate.
"Our children and grandchildren will pay it, plus the interest that accumulates on it," Sessions said of the Katrina aid. Representative Jeff Flake called on Congress to offset spending for Hurricane Katrina relief with funding from lower priority programmes.
Louisiana's Governor has criticised
US lawmakers' responses
"If ever there was a reason to cut spending, this is it," said Flake. "Today Congress appropriated another 50 billion in hurricane relief, and it's just a start," Flake said.
"That's an average contribution of more than 600 dollars from every household in America. Congress has the responsibility to cut spending elsewhere if we are going to commit this amount of money."
Monitor spending plea
Another Republican, Representative Tom Tancredo, introduced legislation to create a special House committee to monitor Katrina-related spending.
"There is no question that billions of dollars are needed - and are needed immediately - to provide relief and reconstruction for Louisiana. But the urgent need of resources does not excuse us from our duty to safeguard the American taxpayers' money," said Tancredo.
"I'm concerned that the federal government has created a situation that is ripe for fraud and abuse."
"Billions of dollars are being handed out to a place where there is severely compromised infrastructure, where local officials have been incompetent in their early response to the emergency, and where there is little if any oversight in administering the funds."
"It is our duty to get relief to persons affected by Hurricane Katrina. But it is political malpractice to spend taxpayers' money without making sure that the aid is getting to the right people," he said.