A source told ESPN NFL Insider Adam Schefter that the extension is for three years and is valued at $36.5 million.
Brown, who turns 33 in August, was set to make $9.75 million in 2018, the final season of the contract the Seahawks inherited when they acquired him in a midseason trade with the Houston Texans last year.
The extension means Brown, who made the Pro Bowl last season for the fourth time, will be under contract through the 2021 season. It comes as All-Pro free safety Earl Thomas continued to hold out for a new deal of his own. Thomas has called for the Seahawks to either extend him or trade him.
The Seahawks hope that keeping Brown in the fold will help solidify an offensive line that has been considered the team's biggest weakness in recent seasons. The left tackle position specifically lacked stability in the season and a half between when Russell Okung departed in free agency and Brown was acquired.
According to ESPN Stats & Information, the Seahawks finished the 2017 season with only 1,027 rushing yards by non-quarterbacks -- the fewest in the NFL since the 2006 Detroit Lions.
On Friday, Seahawks coach Pete Carroll spoke glowingly about what Brown has shown since he arrived in a midseason trade last year.
"Duane made an immediate impression on us when he got here. This is a real leader. He's a real man in that huddle and in the locker room, and we're very, very fortunate to have him," Carroll said. "He's a great worker. He's really, really an astute ballplayer. He's got a great voice and perspective that's gonna help other guys.
"Last year, it was right in the middle of everything [when he was acquired]. He couldn't have the effect, but you could see the potential, and he's just taken off in the offseason and done a great job. He's a big factor for us right now. We just love having him on our team."
Brown missed the Texans' first six games of last season and returned to play in one -- against the Seahawks at CenturyLink Field -- before he was traded to Seattle along with Houston's 2018 fifth-round pick for a 2018 third-rounder and a 2019 second.
At the time of the trade, Seahawks general manager John Schneider said the goal was for Brown to finish his career in Seattle.
Brown gave vague responses this offseason to questions about negotiations on a possible extension. The latest came Thursday after Seattle's first practice of training camp, when he reiterated that he's not worried about it without specifying where things stood.
"I'm just out here working, man. Just focusing on my craft," Brown said. "I'm excited to be out here. This is my first training camp in a couple years because I was injured the year before last, so being able to have a full year with the guys, being out here grinding and working, it's the time where the team, the O-line specifically, we kinda build out chemistry. So being able to be a part of that is huge for me. That's all I'm focusing on right now."
Brown suffered a sprained ankle in his second game with Seattle. Carroll on Friday said Brown showed who he is by playing through the injury for the remainder of the season.
"We hadn't been through the battles with him, but his first indication of 'is he going to be tough, is he going to push,' all that -- he did all that stuff and never even left a doubt," Carroll said. "He's all you're looking for. Fantastic football player, fantastic team member."