Saints linebacker Jonathan Vilma was suspended for the entire 2012 NFL season for his role in the team’s bounty scandal. (Cliff Owen/AP)

Former NFL commissioner Paul Tagliabue on Tuesday overturned the suspensions of four current and former New Orleans Saints players and declined to fine them for their roles in the team’s alleged bounty scandal.

Tagliabue, appointed by Commissioner Roger Goodell to hear the players’ appeals, agreed that New Orleans conducted a program that paid players for hits that injured opponents, and that three Saints — linebacker Jonathan Vilma and defensive linemen Will Smith and Anthony Hargrove — were guilty of conduct detrimental to pro football.

But because “this entire case has been contaminated by the coaches and others in the Saints organization,” Tagliabue wrote that he would not impose fines either.

A fourth player, linebacker Scott Fujita, did not engage in conduct detrimental to the NFL, Tagliabue concluded in his 22-page decision.

“I affirm Commissioner Goodell’s factual findings as to the four players,” Tagliabue wrote in his 22-page ruling. “I conclude that Hargrove, Smith and Vilma — but not Fujita — engaged in ‘conduct detrimental to the integrity of, and public confidence in, the game of professional football.’

“I fully considered but ultimately rejected reducing the suspensions to fines of varying degrees for Hargrove, Smith and Vilma,” Tagliabue added.

None of the players has missed a game because of suspensions. They have been allowed to play while appeals are pending, though Fujita is on injured reserve and Hargrove is not with a team.

A league official called Tagliabue’s ruling the end of the process under the collective bargaining agreement between the NFL and its players’ union.

In May, Goodell suspended current Saints players Vilma and Smith and former Saints players Hargrove and Fujita after concluding that they had participated for three seasons in a program that paid them for big hits that injured opponents. The players denied the allegations and challenged the suspensions in court.

Goodell previously suspended former Saints defensive coordinator Gregg Williams indefinitely; Saints Coach Sean Payton for the entire 2012 season; General Manager Mickey Loomis for eight games and assistant coach Joe Vitt for six games.

After an appeals panel established under the labor agreement ordered Goodell to reconsider the penalties, he reissued them in October with some reductions. Fujita’s suspension was reduced from three games to one. Hargrove’s sanction was reduced from eight games to seven and he was credited with serving the five games he had missed as a free agent. Smith’s four-game suspension and Vilma’s season-long suspension were not altered.

Tagliabue heard only player appeals.

The league issued a written statement Tuesday saying that NFL officials “respect Mr. Tagliabue’s decision.”

The league’s written statement also said: “The decisions have made clear that the Saints operated a bounty program in violation of league rules for three years, that the program endangered player safety, and that the commissioner has the authority under the [collective bargaining agreement] to impose discipline for those actions as conduct detrimental to the league.”

The players’ union issued a statement that said: “We believe that when a fair due process takes place, a fair outcome is the result. . . . Vacating all discipline affirms the players’ unwavering position that all allegations the league made about their alleged ‘intent-to-injure’ were utterly and completely false.”

Saints quarterback Drew Brees wrote on Twitter: “Congratulations to our players for having the suspensions vacated. Unfortunately, there are some things that can never be taken back.”

Tagliabue conducted hearings with testimony from witnesses, including Williams. He ruled that the Saints’ program “included performance rewards for recovering fumbles, interceptions and the like” but “also came to include higher cash incentives to ‘cart-off’ or ‘knockout’ an opposing player.”

Tagliabue wrote that “Saints’ coaches and managers led a deliberate, unprecedented and effective effort to obstruct the NFL’s investigation.”

The former NFL commissioner asserted that he did not “in any degree condone” the behavior of the players, but his decision to vacate their suspensions was based in part on the “severe misconduct” of the team’s coaches.

He cleared Fujita based on a finding that the linebacker participated only in a non-injury, pay-for-performance incentive program. But Tagliabue concluded that there was “insufficient basis to reject Commissioner Goodell’s findings” that Vilma offered a $10,000 bounty on Minnesota Vikings quarterback Brett Favre prior to the NFC title game in January 2010.