BOSTON — The National Football League has agreed to pay $765 million to settle a lawsuit brought by thousands of former players, many suffering from dementia and health problems, who accused the league of hiding the dangers of brain injury while profiting from the sport’s violence.

The deal announced on Thursday ,Aug. 29, comes a week before the NFL begins a new season and could resolve a long-running concern for team owners, who faced the prospect of a possibly lengthy trial that could have delved deeply into how well the league understood the toll that football can take on its players.

Sports business experts described the settlement, which will be paid out over decades, as a modest amount of money for the NFL, believed to generate total revenue of $9 billion or $10 billion a year.

But they also said the more than 4,500 former players who brought their case in U.S. District Court for the Eastern District of Pennsylvania could have a struggled to prove each plaintiff’s health problems was a direct result of years on the playing field.

The settlement will cover all former NFL players but none still in uniform once approved by U.S. District Judge Anita Brody, who in July ordered both sides to meet with mediator Layn Phillips, a retired federal judge.