The 28-year-old, recalled to Nigeria's squad last week after being left out of their victorious African Nations Cup campaign at the start of the year, bought himself out of his deal with La Liga team Levante on Monday.
According to Spanish media, his contract with Levante was worth three million euros.
Martins joined the Spanish club at the beginning of the season on a free transfer from Russia's Rubin Kazan and is their top league scorer with seven goals.
The speedy forward should form an effective strike partnership with US international Eddie Johnson at the Sounders.
Seattle's average league attendance last year was 43,144, making them by far the best supported team in the league.
"The move is consistent with our promise to the fans," majority owner Joe Roth told the team's website.
"Our supporters are the best in Major League Soccer and deserve a team that competes each and every year. Obafemi is an electrifying talent who has international experience at the highest level."
Martins has also played in Germany for VfL Wolfsburg and was on loan with Birmingham City when he scored the winning goal in their shock 2-1 English League Cup final victory over Arsenal at Wembley in 2011.