Bruce Feldman of Sports Illustrated first reported the news and noted the $34.8 million contract includes a $2 million buyout clause for 2017.
Franklin spoke about the extension in the team's news release:
"My family and I are very thankful to be a part of the Penn State community. I am pleased with the progress our program has made in the community, in the classroom and on the field. I look forward to diligently working with President Barron and Director of Athletics Sandy Barbour on implementing a plan that puts our University and our student-athletes in the best position to compete on the field and in life."
Franklin said earlier in August he wasn't going to let the contract discussions distract from his preparations for the upcoming season, per Greg Pickel of Penn Live.
"I'm in football mode now, so I'm focused on the season," he said. "We've been talking about this for a while, and I feel good about it. I don't have any concerns, but my focus is on our team and the 2017 season, completely."
The 45-year-old Pennsylvania native led the Nittany Lions to an 11-3 record, their best mark since 2009, and a Rose Bowl appearance last season. He holds a 25-15 overall record since taking over the program in 2014 and has made it to a bowl game every year.
Penn State's results under Franklin, who previously posted a 24-15 record across three years as the head coach at Vanderbilt, have represented the most consistent signs of stability since the Jerry Sandusky child sex abuse scandal rocked the program late in Joe Paterno's tenure.
Last July, the head coach said some "people," referencing other college football programs, use the Sandusky scandal against the school when recruiting, per Jourdan Rodrigue of Centre Daily. He also said it's a subject that's unlikely to disappear, so it can't impact his day-to-day efforts.
"These things are going to be going on for a number of years," Franklin said. "My focus needs to be on the things that we can control. That's not one of them. For me, answering questions about things that happened 40 years ago when I was 4 years old, I don't know if that’s necessarily the best use of my time or others'."
Penn State finished the 2017 recruiting cycle with the 15th-best class in the country and the fourth-best group among Big Ten schools, according to Scout.com.
The Nittany Lions are set to open the new campaign with a home game at Beaver Stadium against MAC opponent Akron on Sept. 2.