At least 95 percent of the claimants must opt in for the settlement to take effect, The New York Times reported. The deadline is Sept. 30.
U.S. District Judge Alvin Hellerstein gave formal approval to the plan after a daylong hearing that included testimony from those who support the settlement and those who do not.
"It is fair in amount, it is fair in procedure," he said.
The settlement covers emergency workers, including police officers and firefighters, and volunteers who were at the World Trade Center site during rescue and cleanup after the Sept. 11, 2001, terrorist attack.
Some of those who objected to the settlement do not like the method of calculating damages, which combines both the severity of the health problems a victim has with how closely the cause can be tied to the World Trade Center. People with asthma and other respiratory diseases are likely to get more money than those with cancer because causation is clearer, the newspaper said.