The Spanish club have confirmed that the Nigerian striker triggered the buyout clause from his contract with Levante and Martins announced via Twitter that he had joined the MLS outfit.
"Wow... Finally, I can now announce that I have just signed for Sounders FC. A big step to take in my career, it's a big challenge but I'm ready," he wrote.
"I look forward to this new era in my career... I also look forward to meet my new team-mates and the Sounders FC fans, my new family..."
Goal.com has attempted to reach the Sounders for comment, but Seattle have yet to confirm the signing.
Martins, 29, has scored nine goals in all competitions for Levante this season, and played 90 minutes in the Europa League against his former side Rubin Kazan on Thursday.
He is expected to sign as a Designated Player to fill Fredy Montero's shoes, and looks likely to partner up with Eddie Johnson.
That would allow Mauro Rosales to play further back in midfield, after he started as a forward in the club's season-opening loss to Montreal and in the Concacaf Champions League defeat by Mexican side Tigres UANL.