STATE COLLEGE, Pa. (AP) - The NCAA agreed Friday to restore 112 football wins it had stripped from Penn State and Joe Paterno in the Jerry Sandusky child-molestation scandal and to reinstate the venerated late coach as the winningest in major college football history.

The agreement, swiftly approved by the boards of the NCAA and the university after intermittent talks heated up this week, lifts the last of the sanctions imposed in 2012 and wipes away the black marks that had tainted one of the nation's most celebrated college athletics programs.

After more than two years of criticism that the NCAA had overstepped its authority, officials with college sports' governing body did not back down. Instead, they said they were focused on ending litigation that had held up distribution of the university's $60 million fine to fund child abuse-prevention programs.

Before the deal, the NCAA had agreed last year to eliminate some of the sanctions, including reinstating Penn State's full complement of scholarships and letting the team participate in post-season play.

Friday's agreement threw out the rest of the sanctions, including eliminating a five-year probation period and scholarship and transfer rules, and restoring the wins that had been wiped out. It also bowed to Pennsylvania officials' desire to see the $60 million fine spent in Pennsylvania, not spread to abuse-prevention programs around the nation.

The pact emerged just days after a federal judge declined to rule on the constitutionality of the sanctions and weeks before a Pennsylvania court was to hold a trial on the legality of the penalties.

"Hopefully, today we'll begin to make right the damage that has been done," said Pennsylvania Senate Majority Leader Jake Corman, who had sued the NCAA with state Treasurer Rob McCord. "Today is a victory for due process, which was unafforded in this case. Today is a victory for the people of Pennsylvania. Today is a victory for Penn State nation. The NCAA has surrendered."

The unprecedented scope of the sanctions had drawn intense criticism from Penn State alumni and fans who defended Paterno as innocent in the scandal and called the school's athletics program a national model. They accused the NCAA of rushing to judgment to assert its dominance, ultimately punishing people who had nothing to do with Sandusky.

The family of Paterno, who died as the scandal was unfolding, hailed the agreement, while lawyers for Sandusky's victims worried that the NCAA's retreat sent the wrong message. In State College, home to Penn State's sprawling main campus nicknamed Happy Valley, the news was welcome.

Hundreds of students gathered Friday night to celebrate outside Penn State's administration building. They said Paterno didn't deserve to lose his "winningest coach" title and they hoped the new settlement would help the school continue to mend its reputation.

In the agreement, Penn State acknowledged that the NCAA had acted in good faith in the Sandusky matter, and university President Eric Barron said he believed the agency had a legitimate concern about institutional control.

NCAA officials said Friday that their motivation in the deal was to start funding abuse-prevention programs with the fine.

"The victors are those of us who were advocating for the children," said Harris Pastides, an NCAA board member and president of the University of South Carolina.

They did not back off their right to take such action.

"The board felt they had to quickly and decisively put forward a set of sanctions. I hope we never have to do this again," said Kirk Schulz, an NCAA board member and Kansas State's president.

The penalties sprung from the scandal that erupted when Sandusky, a retired assistant coach, was accused of sexually abusing boys, some of them on campus.

Penn State's then-President, Rodney Erickson, agreed to the sanctions in 2012, in the weeks after Sandusky was convicted. Just days earlier, former FBI Director Louis Freeh released a scathing report commissioned by Penn State's trustees, and the school removed an iconic bronze statue of Paterno from the school's Beaver Stadium.

Freeh's report accused Paterno and other top Penn State officials of burying child sex-abuse allegations against Sandusky to avoid bad publicity. The report portrayed the Hall of Fame coach as more deeply involved in the scandal than previously thought.

The alleged cover-up by Paterno, then-university President Graham Spanier and two other Penn State administrators allowed Sandusky to prey on other boys for years, it said.

Paterno was never charged with a crime, although Spanier and the two other former administrators continue to fight charges in court.

Paterno's family called Friday's announcement "a great victory for everyone who has fought for the truth in the Sandusky tragedy."

"This case should always have been about the pursuit of the truth, not the unjust vilification of the culture of a great institution and the scapegoating of coaches, players and administrators who were never given a chance to defend themselves," they said.

Michael Boni, a lawyer for one of the victims who testified at Sandusky's trial, said he supported the restoration of Penn State's scholarships and bowl eligibility last fall, but does not believe Paterno's victories should be reinstated because they were "tarnished" by Sandusky.

He also said he sensed a shift in Penn State's attitude after the criminal case against Sandusky wrapped up and it concluded civil settlements with victims.

"There was a movement away from what I thought was a genuine mea culpa on the part of Penn State, having accepted the NCAA sanctions, and one toward, 'Why did we cave so easily?' That was disappointing," Boni said.

The sanctions eliminated all wins from 1998, when police investigated a mother's complaint that Sandusky had showered with her son, through 2011, Paterno's final season as head coach after six decades with the team and the year Sandusky was charged.

The restored wins include 111 under Paterno and the final victory of 2011, after trustees fired Paterno in the wake of the charges against Sandusky and the team was coached by Tom Bradley. That returns Paterno's record to 409-136-3. He died of lung cancer at 85 shortly after the season ended.

Sandusky was convicted of 45 counts and is now serving a 30- to 60-year prison sentence.