Now the defensive coordinator in St. Louis, Williams and the Saints could be subject to significant penalties, including suspensions, fines and the loss of draft picks.
"It was a terrible mistake, and we knew it was wrong while we were doing it," Williams said. "Instead of getting caught up in it, I should have stopped it. I take full responsibility for my role. I am truly sorry. I have learned a hard lesson and I guarantee that I will never participate in or allow this kind of activity to happen again."
Williams has been known for his aggressive, physical defenses both as a coordinator with four NFL teams and as head coach in Buffalo. Several Redskins told the Washington Post that Williams used a similar system when he was their defensive coordinator.
An NFL investigation found between 22 and 27 defensive players were involved in the program administered by Williams, with the knowledge of coach Sean Payton.
Commissioner Roger Goodell did not hand out any punishment and will meet with the NFL Players Association and individual players to discuss appropriate discipline.
"Health and safety is a paramount issue to the NFLPA," the union said in a statement. "The NFLPA was informed of this investigation by the NFL earlier today and will review the information contained in the league's report."
Williams worked under Buddy Ryan and considers himself a disciple of the former coach who once was accused by Dallas of placing a bounty on some Cowboys.
"I'm not going to apologize for how hard our guys play, and I'm not going to apologize if they're trying to lay the wood on everybody," Williams once said. "When the other team is worried about protecting themselves over protecting the ball, we all like that a lot better."
He went back to coordinating in 2004 in Washington, left in 2008 to joins Jacksonville for one season, then moved to New Orleans just as the Saints were becoming the class of the NFC South.
Several players told The Washington Post on Friday that Williams had a similar bounty program with the Redskins.
Former defensive end Philip Daniels, now as the team's director of player development, said the most he received was $1,500 for a four-sack game against the Dallas Cowboys in 2005; player performance bonuses are outlawed by the NFL.
"I think it is wrong the way they're trying to paint (Williams)," Daniels added. "He never told us to go out there and break a guy's neck or break a guy's leg. It was all in the context of good, hard football."