The 31-year-old Smith joins an already deep stable of edge rushers in Seattle. The Seahawks re-signed Carlos Dunlap and Benson Mayowa earlier this off-season and added Kerry Hyder Jr., who led the San Francisco 49ers in sacks (8.5) last season.
The Seahawks also return L.J. Collier, Alton Robinson, Darrell Taylor, Rasheem Green and star safety Jamal Adams, who led the club with 9.5 sacks last year.
After being reinstated from an indefinite suspension that lasted from 2016-19 for multiple off-field incidents and violations of the NFL's substance abuse policy, Smith signed a one-year contract with the Cowboys ahead of the 2020 season.
Smith started last season with a three-sack performance in Week 3 against the Seahawks, but he finished the year with just five sacks. He was second to star pass-rusher DeMarcus Lawrence on the Cowboys with 33 quarterback pressures.
Smith appeared in every game and played 808 defensive snaps in the 2020-21 campaign. He recorded 48 total tackles, two fumble recoveries and two passes defensed.
The Cowboys informed Smith last month that he would not be re-signed.