"Although we understand the task of healing is just beginning, today's verdict is an important milestone," the statement said. "The community owes a measure of gratitude to the jurors for their diligent service. Our thoughts and prayers continue to be with the victims and their families."
The university, meanwhile, said it had "tremendous respect for the men who came forward to tell their stories publicly."
"No verdict can undo the pain and suffering caused by Mr. Sandusky, but we do hope this judgment helps the victims and their families along their path to healing," Penn State said in a statement.
Penn State said it will invite the victims to participate in a program to facilitate resolution.
"The university wants to provide a forum where the university can privately, expeditiously and fairly address the victims' concerns and compensate them for claims relating to the University."
The Sandusky case has infuriated the Penn State community, not just because of the heinous nature of the crimes, but also because the scandal has unfairly defined the university, students say.
"It's a relief. Now we can begin to heal," Penn State senior Karisa Maxwell said of the verdict. "I've never seen Jerry Sandusky. He has no affect on my education. For people to say he's Penn State is disgusting. That's not the case."
After a week of testimony, during which time witnesses graphically described sexual encounters with Sandusky that they said occurred during their boyhoods, jurors made their decision without ever having heard from Sandusky on the witness stand.
During closing arguments, prosecutors described the ex-Nittany Lions defensive coordinator as a pedophile who preyed on victims using a charity he founded for troubled children, repeatedly abusing young boys in his care.
The defense tried to pick apart the testimony of Mike McQueary, a former graduate assistant who testified that he witnessed Sandusky apparently sodomizing a boy in a university shower.
In a bombshell announcement Thursday evening, Matt Sandusky -- one of Jerry Sandusky's six adopted children -- said through his attorney that he was sexually abused by the former coach, adding that he had been prepared to testify against him.
Legal analysts say the accusation could bring additional charges, including incest charges, against the former coach.
The broader scandal has also brought charges against vice president Gary Schultz and former Athletic Director Tim Curley for perjury and failing to report the abuse.
Eight young men testified, often in disturbingly graphic detail, of how Sandusky forced them to engage in sexual acts in various places, including showers in the Penn State coaches' locker room, hotel rooms and the basement of his home.
On Tuesday, Sandusky's wife told jurors that she could remember at least six of her husband's accusers staying overnight at their house, but that she never witnessed sexual abuse.
The defense challenged the accusers' timetable, questioned the various allegations and called multiple character witness to defend Sandusky's stellar reputation in the community.
Though Friday night's verdict prompted cheers outside the courtroom, inside, the mother of Victim 6 did not claim victory.
"Nobody wins. We've all lost," she said before hugging her son.
CNN's Susan Candiotti, Elisa Roupenian, Ross Levitt, Jason Carroll, Dana Garrett, Laura Dolan, Holly Yan and Anderson Cooper and In Session's Michael Christian and Mayra Cuevas contributed to this report.