The contract is worth up to $5 million for the 31-year-old edge rusher, who joins Seattle after the team lost Boye Mafe in free agency.
Fowler, who visited before the draft, fills Seattle's remaining edge need after the Super Bowl champions did not select a pass rusher with any of their eight picks.
The former third overall pick has 58.5 career sacks and reunites with defensive coordinator Aden Durde after recording three sacks in 17 games for Dallas last season.
Is swapping a young star for a declining veteran a savvy move for the defending champion Seahawks' dynasty plans?
With five key defenders now 29 or older, are the Seahawks building a veteran fortress or risking a defensive collapse?