After more than 5,000 former players sued the NFL seeking damages for head injuries, the league agreed in August to settle the suit. Brody rejected the proposal in January.
"Today's agreement reaffirms the NFL's commitment to provide help to those retired players and their families who are in need, and to do so without the delay, expense and emotional cost associated with protracted litigation," said Anastasia Danias, a senior vice president for the league.
Christopher Seeger and Sol Weiss, who lead the committee of lawyers representing the former players, said they hoped the new proposal would address concerns from players who feared there would be no money left for them if they developed neurocognitive conditions in the future.
"Some of the players were concerned and asking questions about whether they could be in a deal if they weren't sure there would be money there for them 40 years from now if they get sick," Seeger said. "That's what drove these changes."
Retired players would be compensated on a sliding scale based on age, the number of seasons played, and whether post-career injuries might have contributed to cognitive diagnoses.
Maximum awards of $5 million would go to players under 45 who played five or more seasons and require extensive treatment over their lifetimes for conditions such as Parkinson's disease or Lou Gehrig's disease.
Payouts decreasing on a scale would be provided for older players or those who played fewer seasons and had less serious diseases.
The new proposal, however, removes earlier provisions that barred former players from also suing the NCAA or other leagues.
It also includes measures aimed at protecting the NFL from false claims, including the creation of a network of approved doctors on tightened requirements for those making concussion-related diagnoses.
If the judge approves the new plan, it will be sent to all eligible retired players and their beneficiaries, who will decide whether to opt in, object to its terms, or reject it outright. Payments would not be disbursed until all appeals are exhausted.