The $4.3 billion bill cleared its biggest hurdle early in the afternoon when the Senate unexpectedly approved it just 12 days after Republican senators had blocked a more expensive House version from coming to the floor of the Senate for a vote.
In recent days, Republican senators had been under fire for their opposition to the legislation.
The House quickly passed the Senate bill a few hours later, as was widely expected. The vote was 206 to 60, breaking down largely along party lines.
The White House said President Obama would sign the bill into law.
After the Senate vote, a celebration broke out in a room in the Capitol that was packed with emergency workers and 9/11 families, as well as the two senators from New York, Charles E. Schumer and Kirsten E. Gillibrand, and the two senators from New Jersey, Frank R. Lautenberg and Robert Menendez. The senators, all Democrats, were greeted with a huge ovation and repeated chants of “U.S.A.! U.S.A.!”
Mr. Schumer, the state’s senior senator, allowed Ms. Gillibrand to address the group first, in apparent deference to the role she took in the Senate on the 9/11 legislation.
“Our Christmas miracle has arrived,” she said to applause and cheers.
“To the firefighters here, the police officers here, everyone involved in the recovery, all the volunteers, the family members: Thank you!” she continued.
“It was your work, it was your heroism, it was your dedication that made the difference. It was your effort, coming here week after week to tell senators and Congress members about your stories and what you went through.”
The votes came after prolonged aggressive lobbying by top New York officials and lawmakers, police and firefighter groups and 9/11 families, who argued that the nation had a moral obligation to provide medical assistance to rescue workers who spent days, weeks and even months at ground zero.