According to the league, Payton ignored instructions from the NFL and Saints ownership to make sure bounties weren't being paid.
The league also chastised him for choosing to "falsely deny that the program existed," and for attempting to "encourage the false denials by instructing assistants to 'make sure our ducks are in a row.' "
Goodell also banned Saints general manager Mickey Loomis for the first eight regular-season games next season, and assistant coach Joe Vitt for the first six games.
In addition, Goodell fined the Saints $500,000 and took away their second-round draft picks this year and next.
After the NFL first made its investigation public on March 2, Williams admitted to and apologized for running the program while in charge of the Saints' defense from 2009-11. He was hired by the Rams in January.
Goodell will review Williams' status after the upcoming season and decide whether he can return to the league.
The Saints now must decide who will coach the team while Payton is barred, his suspension is effective April 1, and who will make roster moves while Loomis is out.
After the NFL made clear that punishments were looming, Payton and Loomis took the blame for violations that they acknowledged "happened under our watch" and said Saints owner Tom Benson "had nothing to do" with the bounty pool, which reached as much as $50,000 in 2009, the season the Saints won the Super Bowl.
Saints quarterback Drew Brees reacted quickly to the news on Twitter, writing: "I am speechless. Sean Payton is a great man, coach, and mentor … I need to hear an explanation for this punishment." Goodell to NFL clubs: Eliminate bounties
Commissioner Roger Goodell has ordered the owners of all 32 NFL teams to make sure their clubs are not offering bounties like the New Orleans Saints did from 2009-11.
Goodell's memo instructs each team's principal owner and head coach to certify in writing by March 30 that no pay-for-performance system exists.
Goodell said Wednesday that bounty programs "are incompatible with our efforts to promote sportsmanship, fair play, and player safety."
He suspended Saints head coach Sean Payton for the entire 2012 season and GM Mickey Loomis for the first eight regular-season games, while banning former New Orleans defensive coordinator Gregg Williams from the league indefinitely. Williams accepts punishment, apologizes
Rams defensive coordinator Gregg Williams is apologizing to the NFL, to St. Louis coach Jeff Fisher, the Rams organization and football fans in general for running a bounty pool while he was in New Orleans.
Williams was suspended indefinitely on Wednesday by the NFL, and the Rams say he'll be eligible for reinstatement after the season.
In a new statement, Williams does not argue with the terms of the suspension and says, "I accept full responsibility for my actions."
Williams says he will cooperate with the league and its ongoing investigation, and said he'll serve as an advocate for player safety and sportsmanship. Williams added that he'll do anything he can to earn back the respect he has lost. He also says he wants to return to coaching.