The 24-year-old Lynch was drafted 26th overall by the Denver Broncos in 2016, but he started only four games over two disappointing seasons with the team and was waived before the start of the 2018 season.
He remained unsigned, making him eligible to sign a futures contract with Seattle before the start of free agency in March.
A futures contract secures Lynch's rights for the 2019 season. Lynch's agent, Leigh Steinberg, wrote on Twitter that the quarterback "wanted to wait until finding a great fit."
Before signing Lynch, Wilson was the only Seahawks quarterback under contract for 2019.
Brett Hundley, who was Wilson's backup in 2018 after arriving in Seattle in a trade from the Green Bay Packers, is scheduled to be an unrestricted free agent. Alex McGough, a seventh-round pick last year who spent his rookie season on Seattle's practice squad, signed with the Jacksonville Jaguars earlier this week.
Lynch, listed at 6-foot-7 and 244 pounds, had been demoted to third string behind Case Keenum and Chad Kelly before he was waived by the Broncos. In each of his first two seasons, he lost training camp battles to Trevor Siemian to be Denver's starter.
In five regular-season games, Lynch completed 79 of 128 attempts (61.7 percent) for 792 yards, four touchdowns and four interceptions with a 76.7 rating.
"He understands it's a performance business," then-Broncos coach Vance Joseph said in August after officially moving Kelly up the depth chart ahead of Lynch. "He has great potential -- physical potential -- but it's got to equal performance eventually. He understands that. It's a performance league, and everything we do is graded and it's counted."
The Broncos selected Lynch out of Memphis with the pick they acquired in a draft-day trade with Seattle. Denver moved up from No. 31, where the Seahawks took offensive lineman Germain Ifedi.