Williams did not immediately return calls from ESPN seeking comment.
According to the investigation, the players regularly contributed cash into a pool and received improper cash payments of two kinds from the pool, based on their play in the previous week's game.
Williams administered the program with the knowledge of other defensive coaches and occasionally contributed funds, according to the league investigation.
Payments were made for plays such as interceptions and fumble recoveries. But the program also included "bounty" payments for "cart-offs," meaning that the opposing player was carried off the field, and "knockouts," meaning that the opposing player was not able to return.
The investigation showed that the total amount of funds in the pool may have reached $50,000 or more at its height during the 2009 playoffs. The program paid players $1,500 for a "knockout" and $1,000 for a "cart-off," with payouts doubling or tripling during the playoffs.
"The payments here are particularly troubling because they involved not just payments for 'performance,' but also for injuring opposing players," Goodell said in a statement. "The bounty rule promotes two key elements of NFL football: player safety and competitive integrity."
The NFL has a longstanding rule prohibiting "non-contract bonuses," and they violate both the league constitution and bylaws and the collective bargaining agreement with the players' union. Clubs are advised every year of this rule in a memo from the commissioner.
"Our investigation began in early 2010 when allegations were first made that Saints players had targeted opposing players, including Kurt Warner of the Cardinals and Brett Favre of the Vikings," Goodell said in a statement. "Our security department interviewed numerous players and other individuals.
"At the time, those interviewed denied that any such program existed and the player that made the allegation retracted his earlier assertions. As a result, the allegations could not be proven," Goodell said.
"We recently received significant and credible new information and the investigation was re-opened during the latter part of the 2011 season."
According to the NFL investigation, Benson was not initially aware of the bounty program and directed Loomis to make sure it was discontinued immediately. The evidence showed Loomis did not do so, investigators found.
"Similarly, when the initial allegations were discussed with Mr. Loomis in 2010, he denied any knowledge of a bounty program and pledged that he would ensure that no such program was in place. There is no evidence that Mr. Loomis took any effective action to stop these practices," according to the league's findings.
Payton "was not a direct participant in the funding or administration of the program," according to the investigation.
However, Payton "was aware of the allegations, did not make any detailed inquiry or otherwise seek to learn the facts, and failed to stop the bounty program. He never instructed his assistant coaches or players that a bounty program was improper and could not continue," the investigation found.
The investigation included the review of approximately 18,000 documents totaling more than 50,000 pages, interviews of a wide range of individuals and the use of outside forensic experts to verify the authenticity of key documents.
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HAIL THOMAS