The N.C.A.A. on Monday restored Penn State’s postseason eligibility, removing one of the final hurdles in its football team’s path back to normalcy in the aftermath of the child sexual abuse scandal that engulfed the university nearly three years ago.

The decision by the N.C.A.A.’s executive committee means that Penn State will be allowed to participate in a bowl game this season, if it qualifies. It also restores all the scholarships that it stripped from the team.

The move marks a reversal from two years ago, when the N.C.A.A. took the unprecedented — and controversial — step of swiftly barring Penn State’s football team from postseason play for four seasons, slashing its scholarship count and directing $60 million to be put into a national fund for sexual-abuse survivors.

But on Monday, the N.C.A.A. voted to roll back the punishments on the recommendations of former Senator George J. Mitchell, who was hired to monitor Penn State in the aftermath of the case. Mitchell concluded that Penn State had made progress — and that its football players, uninvolved in the abuse case, “bear no personal responsibility” for what transpired in the past.