The deal is for four years and worth $15-16 million, according to the source.
The agreement means the Seahawks will move on from Sebastian Janikowski, who won a preseason competition with Myers last year. Janikowski also is a free agent.
Myers enjoyed a storybook season in 2018. It started with him getting cut and ended with a trip to the Pro Bowl. He was a bargain for the Jets, as he made only $705,000 on a one-year contract.
The Jets claimed Myers on waivers in the preseason after he lost a kicking competition with the Seahawks, who opted to keep Janikowski. The Jets auditioned a few free agents, including the respected Dan Bailey, but they decided to keep Myers.
It was a smart move, as Myers made 33 of 36 field goals, including an NFL-record five of at least 55 yards. All told, he converted six of at least 50 yards, a franchise record. He was the first kicker in Jets history to make the Pro Bowl.
His signature game came in the Jets' Week 6 victory over the Indianapolis Colts, when he became one of eight players in league history with seven field goals in a game. His combined 274 yards on the field goals established a new NFL record.
Oddly, Myers missed as many extra points (three) as he did field goals.
Myers, 27, who played at tiny Marist College in Poughkeepsie, New York, got his start with the Jacksonville Jaguars in 2015. He was their kicker until 2017, when he hit a midseason slump and was released.
Janikowski, who turned 41 on March 2, signed a one-year deal worth $2.015 million with the Seahawks last year after spending his first 18 seasons with the Raiders.
His 2018 season was a mixed bag. Janikowski went 22 of 27 on field-goal attempts for an 81.5 percent conversion rate that ranked 23rd among kickers. Three of those kicks were game-winners as time expired. He was 48 of 51 on extra points.
Janikowski made a pair of field goals in the Seahawks' wild-card loss to the Cowboys before leaving the game for good when he injured his hamstring while attempting a third field goal at the end of the first half. His absence forced the Seahawks to go for two on their two second-half touchdowns as punter Michael Dickson handled the ensuing kickoffs.
ESPN's Rich Cimini and Brady Henderson contributed to this report.