Dumervil's 2013 salary was cut from $12 million to $8 million, according to ESPN NFL Insider Adam Schefter. Had Dumervil not agreed to the restructured deal by 4 p.m. ET, he faced the prospect of getting released.
Dumervil's deal also includes a $3.5 million guarantee on the second day of the league year in 2014.
"It's not all about dollars. But when it's way out of whack? Then it's so out of whack that you've got to say: That [salary] can't be it," Elway had said Thursday, according to the Denver Post. "Especially when you look at the market and what's out there now. It's so far out of whack. Hopefully, he realizes that."
Dumervil signed a six-year, $61.5 million contract in 2010 when Josh McDaniels was coaching the team and before Elway joined the Denver front office.
Dumervil had 11 sacks last season, second on the team behind Von Miller. Dumervil led the league with 17 sacks in 2009.
The Broncos need more cap space while trying to shore up their interior defensive line, cornerback and running back positions. Peyton Manning will earn $20 million in 2013, and if the Broncos had Dumervil play at his current number, those two would've accounted for more than one-quarter of their cap space.
Among the pass-rushers on the market this season include Manning's former teammate with the Colts, Dwight Freeney.
Information from The Associated Press was used in this report.