The Bengals acquired offensive lineman B.J. Finney and a seventh-round pick in the 2021 NFL Draft in exchange for Dunlap, who leaves the franchise as its career sacks leader.
Under the league's COVID-19 protocols, the earliest Dunlap could make his Seahawks debut is Week 9 against the Buffalo Bills.
"I'm not going to lie, I'm nervous as hell but I'm excited," Dunlap said on his Instagram story about joining Seattle. "... It's all up from here. It's all up from here. Let's go. I get to play. Above all, I get to play."
Dunlap -- a second-round pick in the 2010 draft out of Florida -- had grown increasingly frustrated with his role in the Bengals' defense. He had come off the bench in each of the past three games.
The two-time Pro Bowl defensive end also posted a property listing shortly after the Bengals' loss to the Cleveland Browns on Sunday. He later deleted the posts.
"Carlos has done a lot of great things for this organization and the community. He deserves to go out the right way," Bengals head coach Zac Taylor told reporters Wednesday. "He's being sent to a team that's really a great organization. They're in the hunt right now. They've got a great record and he'll have a chance to help."
Dunlap, 31, had two years remaining on a contract extension that was scheduled to expire at the end of the 2021 season. In his 11-year tenure with the Bengals, he tallied 489 total tackles, 82.5 sacks and 20 forced fumbles.