The Packers' release didn't include contract details but the Milwaukee Journal Sentinel said the agreement covered five years, through the 2018 season, and totaled $66 million.
Matthews confirmed the contract on his Twitter account, writing, "Trivial among the recent tragic news, but happy to continue me career in Green Bay!"
Matthews, who turns 27 next month, was the 26th overall selection in the 2009 draft. He's played 58 games for the Packers, totaling 42.5 sacks, four interceptions and 204 tackles.
He was named All-Pro in 2010 and 2012 and has been voted to the Pro Bowl each of his four seasons.
"Congratulations to Clay, who has quickly developed into a core member of our team," Packers Coach Mike McCarthy said. "His accomplishments and the example he sets on and off the field will be vital to our continued success. We look forward to the rest of his Packers career."