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.”