Terms of the extension weren't disclosed by the team, but a source confirmed to ESPN that the extension is for five years and worth about $65 million in new money, including $31 million guaranteed. Fox Sports had earlier reported terms of the deal.
A source close to the deal told ESPN.com's Darren Rovell that Matthews will receive $22 million by the end of 2013 and $27 million in the next 12 months.
"It feels good," Matthews said Wednesday during a news conference inside the Packers locker room. "It's funny, because not a whole lot has changed. I'm happy about it, but for me, it's nice, it's very humbling and it's a blessing, but it's business as usual for me. I'm glad that they have put their trust in me and belief in me in awarding me this, but at the same time you're going to get the same type of unwavering perseverance on the field and dedication that I'm going to bring day in and day out. I feel good but not much has changed.
Matthews tweeted a picture of himself signing the contract before it was officially announced by the team.
He wrote: "Trivial amongst the recent tragic news, but happy to continue my career in Green Bay!"
Matthews was set to earn a base of $3.73 million this season in the final year of his rookie deal, signed after the Packers made him the 26th pick in the 2009 draft
"Clay has been a productive member of our team and we are pleased to be able to come to an agreement that will extend his Packers career," general manager Ted Thompson said in a statement.
Matthews, 26, has 42.5 sacks in his four seasons with the Packers, including 13 last season. He has 204 tackles, seven forced fumbles and four interceptions in 58 career games since being drafted out of USC.
"Congratulations to Clay, who has quickly developed into a core member of our team," coach Mike McCarthy said in a statement. "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."
The Packers are also working on an extension for Aaron Rodgers, with sources saying last month the sides were closing in on a long-term deal that would make the quarterback the highest-paid player in NFL history.
"Hopefully, that's the next order of business," Matthews said about Rodgers' extension. "Being good friends with him, represented by the same agent, who knows, hopefully, that's sooner than later."
Matthews said he didn't think the team would be hamstrung by big contracts for its two biggest stars, and that the team's draft-and-develop philosophy would keep it competitive.
"One thing this organization does well. I know we catch a little heat sometimes that we like to build through the draft and develop our players, and we've done a great job of that," Matthews said. "Our free agents are the ones who were up on their contracts. It's no different than Aaron, myself or whoever's up next. I'll leave that to them, but for the most part we've had some success here over the last few years in maintaining key players and I don't see it to be any different."
Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.