The surprise announcement, linked to progress the school has made reforming its athletics programs, moved the university a step farther away from the fallout from Sandusky, the former assistant coach convicted of sexual abuse of 10 boys, including acts inside university facilities.
The scandal badly tarnished what had been one of college sports' most respected programs and led to charges of a criminal coverup against former university administrators Graham Spanier, Gary Schultz and Tim Curley, whose cases are still pending, and the firing of Hall of Fame coach Joe Paterno.
Penn State had been halfway through a four-year post-season ban handed down during the summer of 2012. Some of the scholarships were restored earlier than expected a year ago.
The university still must pay a $60 million fine, vacate 111 wins that came under Paterno, plus another under interim coach Tom Bradley, and the school will remain under monitoring.
The decision by the NCAA's Executive Committee followed a recommendation by former U.S. Sen. George Mitchell, whose second annual report as Penn State's athletics integrity monitor concluded the university was in compliance with a 2012 agreement and consent decree.
"Senator Mitchell's report and recommendations, along with the actions taken by the NCAA today, are a recognition of the hard work of many over the past two years to make Penn State a stronger institution," Penn State President Eric Barron, who took over in February.
Mitchell said the school had made progress toward implementing a new human resources system, "fostering an ethical culture" and improving security at its sports facilities. His own five-year oversight role, scheduled to continue to 2017, may end earlier as a result of the progress that has been made, he said.
Mitchell said his recommendation was focused on aspects of the penalties that affect student-athletes, many of whom stayed at Penn State despite the ability to transfer without penalty.
"In light of Penn State's responsiveness to its obligations and the many improvements it has instituted, I believe these student-athletes should have the opportunity to play in the post-season should they earn it on the field this year," Mitchell wrote.
His 58-page report said incidents involving the football team this year included only minor infractions.
In State College, junior kinesiology major Daniel Zambanini said seeing the news on television gave him a moment of shock.
"The sanctions kind of held the Sandusky scandal like it was a big black cloud that hung over the university because every year, every time they mentioned Penn State, they mentioned the sanctions," Zambanini said.
He said removal of the post-season ban "just takes that weight off our shoulders and you can kind of just be Penn State once more."
The penalties against Penn State were unprecedented in many ways and, because of that, not well-received by many in college sports. While the NCAA cited lack of institutional control, Penn State's missteps had nothing to do with competition and the areas that usually fall under the NCAA's jurisdiction.
"The biggest problem I had was the effect on the student athletes in the program," said former Big 12 commissioner Dan Beebe, who worked in NCAA enforcement during the 1980s, including on the SMU football death penalty case. "They (Penn State's players) weren't involved in a program that was cheating against their rivals and now all of sudden they're not able to participate in post-season."
The NCAA cutting the penalties down is also unusual. Beebe and Mike Gilleran, a sports law and ethics professor at Santa Clara University who worked in NCAA enforcement during the 1970s and '80s, said they were concerned the latest move would set another precedent.
"So what happens now when one of your old schools," Gilleran said, referring to Beebe's time in the Big 12, "gets whacked? 'OK, we'll take that penalty with the understanding that we will be model citizens and we will expect the treatment that Penn State got.'"
Beebe said rolling back the sanctions gives the appearance of the NCAA acknowledging it might have overreached by getting involved with the Sandusky scandal.
"My first blush is I don't know how it could be perceived differently," he said. "'I'd be very curious to dive into (the NCAA's) rationale."
On Friday, the NCAA said in a Pennsylvania state court filing it is willing to let the state government control the $60 million fine Penn State is paying under the consent decree. The NCAA wants the judge to dismiss a lawsuit filed by state officials seeking to enforce a 2013 state law that requires the money remain in the state.
If the judge agrees, the NCAA said it also will move to end a federal lawsuit against Gov. Tom Corbett and others that challenges that same law.
Penn State went 15-9 during the first two seasons of the sanctions under coach Bill O'Brien, who was hired to replace Paterno.
Paterno was the winningest coach in major college football history when he was fired not long after Sandusky, his former defensive co-ordinator, was charged November 2011. Paterno died in January 2012 and lost his record when the NCAA vacated those 111 victories
O'Brien left for the Houston Texans of the NFL after last season and James Franklin was hired away from Vanderbilt to take his place.
Penn State is 2-0 this season. If the Nittany Lions win the East division, they will be eligible to play in the Big Ten championship game.
Franklin said in a statement the team appreciates the opportunity.
"This team plays for each other. We play for Penn State, our families, the former players, our students, alumni, fans and the community," he said.
Scolforo reported from Harrisburg, Pennsylvania.