The 36-year-old right-hander from the Dominican Republic signed for $14 million, according to media reports.
Rodney went 5-4 with 37 saves and a 3.38 earned run average for the Tampa Bay Rays last season, following a breakthrough season in which he saved 48 games with a miniscule 0.60 ERA.
Rodney's signing came in the wake of news that Seattle outfielder Franklin Gutierrez will miss the entire 2014 season due to ongoing gastrointestinal issues.
Adding the hard-throwing closer was the latest move in a busy offseason for the Mariners, striving to improve on their 71-91 record of last year.
Seattle made a huge splash by signing slugging free agent second baseman Robinson Cano to a 10-year, $240 million deal, also added power-hitting outfielder/first baseman Corey Hart to liven up their offense.
(Reporting By Andrew Both in Cary, North Carolina; Editing by Larry Fine)