C-SPAN reported the Disaster Relief and Appropriations Act passed 241-180, with 179 Republicans and one Democrat casting "no" votes.
The House action sends the bill to the Democrat-controlled Senate, which had previously passed its own version and is expected to give its stamp of approval to the House version Jan. 22.
Earlier, the House voted 367-52 in favor of a rule for further debate on the measure, clearing the way for the final vote, The Hill reported.
Although most Republicans and Democrats urged support for the bill, Rep. Tom McClintock, R-Calif., argued against it, saying billions of dollars would be spent on longer-term storm mitigation matters, rather than on immediate relief from the storm that struck the region in October, The Hill reported.
"According to the Congressional Budget Office, more than 90 percent of this money won't even be spent this year," McClintock said. "That's not emergency relief."
Rep. Bill Pascrell, D-N.J., said the governors of New York, New Jersey and Connecticut had been very specific in describing their states' needs.
"It's no grab bag," Pascrell said of the bill. "That's an insult to the Northeastern states that were hit by this tremendous storm."
The bill includes $17 billion for immediate recovery needs, C-SPAN noted, with $33.7 billion more for longer-term projects.
Before the vote, Rep. Peter King, R-N.Y., told The Hill he was confident the House would approve the full amount of aid requested.
King, who represents hard-hit central Long Island, had told The Hill amendments by GOP House colleagues could kill the bill.
"We were told the bill was coming up as is," he said.
Conservative House Republicans outside the Northeast had submitted 92 amendments to the package to either cut spending they saw as non-essential or demand budget cuts in popular programs elsewhere to offset the Sandy package.
Congress has historically not offset disaster relief with spending cuts, and lawmakers from states hit by Sandy expressed outrage by proposals to do so now.
The White House Monday urged the House to steer clear of requiring offsets.
The House separately approved $9.7 billion Jan. 4 to help pay flood insurance claims from the storm.
Sandy, which struck the Northeast Oct. 29, has been blamed for 131 deaths and $63 billion to more than $80 billion in damages.
It wiped out entire communities in coastal New York and New Jersey, paralyzed mass transit systems and left tens of thousands of people homeless. Power was cut to more than 8 million homes in 16 states and the District of Columbia.