Christoper Seeger, who represented former N.F.L. players in a concussion settlement, outside of the United States Courthouse in Philadelphia in 2014. The Supreme Court declined to review the case on Monday. Credit Matt Rourke/Associated Press

The United States Supreme Court on Monday denied a request to review the N.F.L. ’s settlement with retired players who had accused the league of hiding the dangers of head trauma, paving the way for some players with brain ailments to begin receiving payments of as much as $5 million.

The decision ends a contentious five-year fight between the league and many former players, some of whom are suffering from Alzheimer’s, amyotrophic lateral sclerosis and other debilitating conditions. The settlement, worth perhaps as much as $1 billion, covers nearly every former player for the next 65 years; the league’s actuaries estimated that just under 30 percent of them could develop Alzheimer’s or other conditions covered in the settlement.

The agreement is by far the largest concussion-related settlement, and a landmark in light of the league’s repeated denials, made over many years, of the links between repeated head trauma and brain disease. The N.C.A.A. agreed to a far smaller settlement, while the N.H.L. is still fighting its former players, who have filed a suit largely similar to the one brought by the retired N.F.L. players.

“This decision means that, finally, retired N.F.L. players will receive much-needed care and support for the serious neurocognitive injuries they are facing,” Christopher Seeger, one of the lead lawyers for the retired players, said in a statement. “These courageous men and their families, who in the face of great adversity took on the N.F.L., have made history.”

The Supreme Court was asked to review the settlement by a subset of retired players who believed, among other things, that the agreement unfairly excluded players who received a diagnosis of a severe brain disease linked to head hits, chronic traumatic encephalopathy, after Judge Anita B. Brody of United States District Court approved the settlement last year. They also argued that the settlement did not adequately account for scientific innovations that may allow for C.T.E. to be diagnosed in people while they are alive. Currently, the disease can be confirmed only in autopsies.

The United States Court of Appeals for the Third Circuit already rejected those arguments, and the Supreme Court, without comment, followed suit by refusing to review the case.

“We are pleased that the Supreme Court has decided not to review the unanimous and well-reasoned decisions of Judge Brody and the Third Circuit approving the settlement of this litigation,” the league said in a statement. “We look forward to working with class counsel and Judge Brody to implement the settlement and provide the important benefits that our retired players and their families have been waiting to receive.”Cullin O’Brien, the lawyer who represented the former N.F.L. player Cookie Gilchrist in the petition to the Supreme Court, had no comment. He and other lawyers representing players who petitioned the court could ask the court to reconsider its refusal, but legal experts said that would be a long shot.

Still, the agreement did not come easily. For several years, the N.F.L. insisted that arbitrators, not the courts, should be used to settle disputes between players and the league. The players would likely have had to prove that the concussions they received in the N.F.L. led directly to their current conditions.

After Judge Brody questioned whether the initial agreement, worth $765 million, would be enough to cover every player, the league agreed to pay an unlimited amount of damages. Some estimates suggest that the league could pay $1 billion to cover all claims.

Critically, the players will not have to prove that they sustained any concussions while playing in the N.F.L., or whether those concussions led to their ailments. The N.F.L., faced with the potentially damaging possibility of players testifying on the stand about their brain injuries and ailments, agreed to settle the case in August 2013.

Judge Brody still must rule on the status of more than 100 former players who opted out of the settlement. She also must rule on the $112 million payment that the N.F.L. has agreed to pay the plaintiffs’ lawyers.

Starting next month, the league must make six monthly deposits of $20 million into a special account for players covered by the settlement. By April, the plaintiffs’ lawyers must set up the apparatus to allow players to start filing claims. Mr. Seeger said players with diseases that have already been diagnosed should receive checks within weeks after filing their paperwork.

Mr. Seeger said he was negotiating with Medicare , which is allowed in class-action cases of this kind to recoup its medical expenses already spent. As he is negotiating on behalf of a large group of about 20,000 ex-players, Mr. Seeger said, he expects Medicare to offer a substantial discount. Those so-called medical liens would be deducted from any lump-sum settlements.

A version of this article appears in print on December 13, 2016, on page B8 of the New York edition with the headline: N.F.L. Concussion Payouts Clear a Final Roadblock.

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