Dockett, 34 in May, missed the entire 2014 season after tearing his ACL in August. The organization will save $6.8 million in salary-cap space by trimming his $6.55 million salary.
In his prime, Dockett was a versatile three-time Pro Bowl selection capable of playing end and tackle.
Although the two sides were unable to reach agreement on a restructured contract, it's still possible that Dockett will return to the Bird Gang on a more cap-friendly deal after testing the market.
"We have been very clear about our feelings for Darnell and our desire to have him back," general Manager Steve Keim said in a statement, via the team's official website. "After speaking with him and his representatives, we decided that this move today makes the most sense for both the team and the player and allows each to keep all of its options open."