The team has also been fined $500,000 and will have to give up its second-round picks in the 2012 and 2013 NFL Drafts.
The league said in a news release that the involvement of individual players in the program is still being reviewed, and that any discipline will be announced at a future time.
In addition, Saints assistant head coach Joe Vitt has been suspended without pay for the first six games of the 2012 season.
Payton's suspension will begin April 1 and last for the entire 2012 season. Loomis' suspension, which is also without pay, will be for the first eight games of the 2012 season.
Williams, who was hired to be the St. Louis Rams' defensive coordinator earlier this year, will have his status reviewed by NFL Commissioner Roger Goodell after the 2012 regular season has ended, according to the release. Goodell will then decide if Williams should be reinstated.
Sources close to Williams told NFL Network insider Jason La Canfora that they were shocked by the news. The sources said they had been expecting a shorter suspension, something like a month or six games, and had been hoping for something that would last less than half a season.
The release spelled out Williams' involvement in the program, which was extensive. According to the release, he helped fund the pool that rewards came from, in addition to being the architect of the scheme.
Saints quarterback Drew Brees reacted very strongly to Payton's punishment.
"I am speechless," Brees wrote via his Twitter account. "Sean Payton is a great man, coach, and mentor. The best there is. I need to hear an explanation for this punishment."
Williams and Vitt also "misled" the league in its attempts to investigate the program, and Williams kept the program going in 2010.
It had already been known that Brett Favre and Kurt Warner had been among the quarterbacks targeted by the program. On Wednesday, the league's release revealed that the Panthers' Cam Newton and the Packers' Aaron Rodgers had also been targeted.
The NFL also issued a news release in which it announced that the rest of the teams in the league have been told by Goodell that they must ensure bounty programs are not in place. Owners and head coaches are required to provide a written guarantee to Goodell by March 30.
"Bounty programs have no place in our game," Goodell said in that release. "They are incompatible with our efforts to promote sportsmanship, fair play, and player safety."
The NFL revealed March 2 the findings of a lengthy investigation into a Saints "bounty" program that gave thousands of dollars in payoffs to players for hits that knocked opponents out of games. The program, administered by Williams, reached its height in 2009, the season the Saints won the Super Bowl.
The program ran in violation of league rules, and the investigation showed that Saints players received $1,500 for a "knockout" hit and $1,000 for a "cart-off" hit, with payouts doubling or tripling during the team's three playoff appearances.